100 results found for "radical-variable" in Class 10.
एक चर के बहुपद में चर की घातें कैसी होनी चाहिए?
What should the powers of the variable be in a polynomial in one variable?
#powers
#definition
#polynomial
A ऋणात्मक पूर्णांक / Negative integers
B भिन्न संख्याएं / Fractions
C अऋणात्मक पूर्णांक / Non-negative integers
D केवल अभाज्य संख्याएं / Only prime numbers
Explanation opens after your attempt
Correct Answer
C. अऋणात्मक पूर्णांक / Non-negative integers
Explanation
Simple Explanation
बहुपद में चर की घातें \(0,1,2,\ldots\) जैसी अऋणात्मक पूर्णांक होती हैं। यही बहुपद की मूल पहचान है। / In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the basic identification rule.
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बहुपद (p(u)=13u-3 -2u+9) में चर कौन सा है?
What is the variable in the polynomial (p(u)=13u-3 -2u+9)?
#variable
#one variable
#polynomial
A (p)
B (u)
C (13)
D (9)
Explanation opens after your attempt
Explanation
Simple Explanation
जिस अक्षर के मान बदल सकते हैं वह चर होता है। यहां चर (u) है। / The letter whose values can change is the variable. Here the variable is (u).
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बहुपद (p(t)=6t-2 -7t+3) में चर कौन सा है?
What is the variable in the polynomial (p(t)=6t-2 -7t+3)?
#variable
#one variable
#polynomial
A (p)
B (t)
C (6)
D (3)
Explanation opens after your attempt
Explanation
Simple Explanation
जिस अक्षर का मान बदल सकता है वह चर है। यहां चर (t) है। / The letter whose value can vary is the variable. Here the variable is (t).
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निम्न में से एक चर वाला बहुपद कौन सा नहीं है?
Which of the following is not a polynomial in one variable?
#one variable
#two variables
#identification
A \(2x^2+3x+1\)
B \(5t^3-t\)
C \(x^2+y+1\)
D (9z-4)
Explanation opens after your attempt
Correct Answer
C. \(x^2+y+1\)
Explanation
Simple Explanation
\(x^2+y+1\) में दो चर (x) और (y) हैं। इसलिए यह एक चर वाला बहुपद नहीं है। / \(x^2+y+1\) has two variables (x) and (y). Therefore it is not a polynomial in one variable.
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इनमें से कौन सा एक चर में बहुपद है?
Which of the following is a polynomial in one variable?
#polynomial
#one variable
#identification
A (p(x)=3x-2 -5x+7)
B (p(x)=\frac{2}{x}+1)
C (p(x)=\sqrt{x}+4)
D (p(x)=x^{-2}+3)
Explanation opens after your attempt
Correct Answer
A. (p(x)=3x-2 -5x+7)
Explanation
Simple Explanation
एक चर के बहुपद में चर की घात केवल अशून्य पूर्णांक या शून्य होती है। परीक्षा में ऋणात्मक घात और मूल से बचें। / In a polynomial in one variable, powers of the variable are non-negative integers. In exams, reject negative powers and roots of the variable.
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कौन सा बहुपद एक चर (x) में है?
Which polynomial is in one variable (x)?
#polynomials
#one-variable
#easy
#concept
A \(x^2+2x+1\)
B (x+y+1)
C \(a^2+b^2\)
D (xy+3)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x+1\)
Explanation
Simple Explanation
एक चर (x) में बहुपद में केवल (x) चर होता है। अन्य विकल्पों में एक से अधिक चर हैं। / A polynomial in one variable (x) contains only the variable (x). The other options have more than one variable.
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बहुपद (p(t)=8t-2 -3t+4) में चर कौन-सा है?
Which is the variable in the polynomial (p(t)=8t-2 -3t+4)?
#variable
#polynomial_notation
#basics
A (p)
B (t)
C (8)
D (4)
Explanation opens after your attempt
Explanation
Simple Explanation
(p(t)) में बदलने वाला चिन्ह (t) है। इसलिए चर (t) है। / In (p(t)), the changing symbol is (t). So the variable is (t).
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बोस्टन टी पार्टी को अमेरिकी क्रांति की दिशा में उग्र कदम क्यों माना जाता है?
Why is the Boston Tea Party considered a radical step toward the American Revolution?
#world history
#revolutions
#american revolution
#boston tea party
A इसमें उपनिवेशवासियों ने ब्रिटिश कर नीति का प्रत्यक्ष विरोध किया / Colonists directly opposed British tax policy
B इसमें ब्रिटेन ने सभी कर समाप्त कर दिए / Britain abolished all taxes in it
C इसमें फ्रांस ने अमेरिका छोड़ दिया / France left America in it
D इसमें उपनिवेशों ने राजा की पूजा शुरू की / Colonies began worshipping the king in it
Explanation opens after your attempt
Correct Answer
A. इसमें उपनिवेशवासियों ने ब्रिटिश कर नीति का प्रत्यक्ष विरोध किया / Colonists directly opposed British tax policy
Explanation
Simple Explanation
बोस्टन टी पार्टी ब्रिटिश कराधान के विरुद्ध प्रत्यक्ष औपनिवेशिक प्रतिरोध थी। परीक्षा में इसे कर विरोध और असहयोग से जोड़ें। / The Boston Tea Party was direct colonial resistance against British taxation. In exams, link it with tax protest and non-cooperation.
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कौन सा व्यंजक बहुपद नहीं है क्योंकि चर की घात भिन्न है?
Which expression is not a polynomial because the variable has a fractional power?
#not polynomial
#fractional power
#definition
A \(x^4-2x+5\)
B \(3x^2+\sqrt{2}x-7\)
C \(x^{\frac{3}{2}}+x+1\)
D \(9x^3-4x^2\)
Explanation opens after your attempt
Correct Answer
C. \(x^{\frac{3}{2}}+x+1\)
Explanation
Simple Explanation
\(x^{\frac{3}{2}}\) में चर की घात भिन्न है, इसलिए यह बहुपद नहीं है। बहुपद में घातें अऋणात्मक पूर्णांक होती हैं। / In \(x^{\frac{3}{2}}\), the power of the variable is fractional, so it is not a polynomial. In a polynomial, powers are non-negative integers.
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कौन सा विकल्प एक चर में बहुपद है लेकिन रैखिक नहीं है?
Which option is a polynomial in one variable but not linear?
#classification
#quadratic
#not linear
A (5x-8)
B \(x^2+2x+3\)
C \(x+\frac{1}{x}\)
D \(\sqrt{x}+2\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+2x+3\)
Explanation
Simple Explanation
\(x^2+2x+3\) बहुपद है और इसकी घात (2) है। इसलिए यह रैखिक नहीं है। / \(x^2+2x+3\) is a polynomial and its degree is (2). Therefore it is not linear.
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निम्न में से कौन सा बहुपद (x) में है लेकिन (y) में नहीं है?
Which of the following is a polynomial in (x) but not in (y)?
#one-variable
#variable-identification
#polynomial
A \(x^2+3x+1\)
B \(y^2+3y+1\)
C (xy+1)
D (x+y+1)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+1\)
Explanation
Simple Explanation
\(x^2+3x+1\) में केवल (x) चर है। इसलिए यह (x) में एक चर वाला बहुपद है। / \(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).
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कौन सा विकल्प एक चर में बहुपद है लेकिन द्विघात नहीं है?
Which option is a polynomial in one variable but not quadratic?
#classification
#cubic
#not quadratic
A \(x^2+2x+1\)
B \(4x^3+x-9\)
C \(\frac{1}{x}+2\)
D \(\sqrt{x}+3\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3+x-9\)
Explanation
Simple Explanation
\(4x^3+x-9\) बहुपद है और इसकी घात (3) है। इसलिए यह द्विघात नहीं है। / \(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.
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कौन-सा व्यंजक एक चर वाला बहुपद है जिसमें वास्तविक गुणांक हैं?
Which expression is a polynomial in one variable with real coefficients?
#real_coefficients
#polynomial_identification
#irrational_coefficient
A \(\sqrt{2}x^2-3x+1\)
B \(\sqrt{x}+2\)
C \(x^{-2}+1\)
D \(\frac{1}{x}+3\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}x^2-3x+1\)
Explanation
Simple Explanation
\(\sqrt{2}\) एक वास्तविक संख्या है और (x) की घातें पूर्ण संख्याएँ हैं। इसलिए यह बहुपद है। / \(\sqrt{2}\) is a real number and the powers of (x) are whole numbers. So it is a polynomial.
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि चर हर में है?
Which expression is not a polynomial because the variable is in the denominator?
#variable_denominator
#not_polynomial
#negative_power
A \(x^2+2\)
B \(\frac{3}{x}+1\)
C (4x-5)
D \(8x^3\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{x}+1\)
Explanation
Simple Explanation
\(\frac{3}{x}=3x^{-1}\) है और चर की घात ऋणात्मक है। इसलिए यह बहुपद नहीं है। / \(\frac{3}{x}=3x^{-1}\), so the variable has a negative power. Therefore it is not a polynomial.
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कौन-सा व्यंजक (z) में एक चर वाला बहुपद है?
Which expression is a polynomial in one variable (z)?
#one_variable
#polynomial_identification
#z_variable
A \(z^4-2z+1\)
B \(z^{-2}+3\)
C \(\frac{1}{z}+5\)
D (z+w)
Explanation opens after your attempt
Correct Answer
A. \(z^4-2z+1\)
Explanation
Simple Explanation
\(z^4-2z+1\) में केवल (z) है और घातें ऋणात्मक नहीं हैं। इसलिए यह (z) में बहुपद है। / The expression \(z^4-2z+1\) has only (z) and no negative powers. So it is a polynomial in (z).
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\(2x^2+3xy+1\) एक चर वाला बहुपद क्यों नहीं है?
Why is \(2x^2+3xy+1\) not a polynomial in one variable?
#one_variable
#not_polynomial
#concept
A क्योंकि इसमें दो चर हैं / Because it has two variables
B क्योंकि इसमें कोई स्थिर पद नहीं है / Because it has no constant term
C क्योंकि इसकी घात (2) है / Because its degree is (2)
D क्योंकि गुणांक वास्तविक नहीं हैं / Because coefficients are not real
Explanation opens after your attempt
Correct Answer
A. क्योंकि इसमें दो चर हैं / Because it has two variables
Explanation
Simple Explanation
इसमें (x) और (y) दोनों चर हैं। एक चर वाले बहुपद में केवल एक ही चर होना चाहिए। / It contains both (x) and (y). A polynomial in one variable should contain only one variable.
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कौन-सा व्यंजक (x) में एक चर वाला बहुपद है?
Which expression is a polynomial in one variable (x)?
#polynomials
#one_variable
#identification
A \(3x^2-5x+7\)
B \(\frac{2}{x}+1\)
C \(\sqrt{x}+4\)
D (x+y)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-5x+7\)
Explanation
Simple Explanation
\(3x^2-5x+7\) में केवल (x) है और घातें पूर्ण संख्याएँ हैं। परीक्षा में चर की घात ऋणात्मक या भिन्न नहीं होनी चाहिए। / The expression \(3x^2-5x+7\) has only (x) and non-negative integer powers. In exams, the variable power must not be negative or fractional.
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यदि (p(x)=x-4 -5x-2 +4) है, तो (p(x)) का घात कितना है?
If (p(x)=x-4 -5x-2 +4), what is the degree of (p(x))?
#degree
#polynomial
#one-variable
A (4)
B (2)
C (5)
D (0)
Explanation opens after your attempt
Explanation
Simple Explanation
सबसे बड़ी घात \(x^4\) है, इसलिए घात (4) है। शून्य गुणांक वाले पदों को घात तय करने में नहीं गिनते। / The highest power is \(x^4\), so the degree is (4). Terms with zero coefficients do not affect the degree.
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यदि (p(x)=ax-2 +bx+c) में \(a\neq0\) है और (p(1)=p(-1)=0) है, तो (b) का मान क्या होगा?
If (p(x)=ax-2 +bx+c) with \(a\neq0\) and (p(1)=p(-1)=0), what is the value of (b)?
#polynomials
#one-variable
#values
A (0)
B (a)
C (c)
D (-a)
Explanation opens after your attempt
Explanation
Simple Explanation
(p(1)=a+b+c) और (p(-1)=a-b+c) हैं, घटाने पर (2b=0) मिलता है। परीक्षा में सममित मानों पर जोड़-घटाव जल्दी करें। / (p(1)=a+b+c) and (p(-1)=a-b+c); subtracting gives (2b=0). In exams, use addition or subtraction for symmetric inputs.
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निम्न में से (y) में बहुपद कौन सा है?
Which of the following is a polynomial in (y)?
#polynomial-in-y
#one-variable
A \(y^2-3y+2\)
B \(\frac{1}{y}+4\)
C \(\sqrt{y}+5\)
D \(y^{-2}+1\)
Explanation opens after your attempt
Correct Answer
A. \(y^2-3y+2\)
Explanation
Simple Explanation
\(y^2-3y+2\) में (y) की घातें पूर्ण संख्याएँ हैं। बहुपद किसी एक चर जैसे (y) में भी हो सकता है। / In \(y^2-3y+2\), the powers of (y) are whole numbers. A polynomial can be in one variable such as (y).
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क्या \(4x^2-3\sqrt{x}+1\) (x) में बहुपद है?
Is \(4x^2-3\sqrt{x}+1\) a polynomial in (x)?
#not-polynomial
#root-variable
A हाँ / Yes
B नहीं / No
C केवल जब (x) धनात्मक हो / Only when (x) is positive
D केवल जब (x=1) हो / Only when (x=1)
Explanation opens after your attempt
Correct Answer
B. नहीं / No
Explanation
Simple Explanation
\(\sqrt{x}=x^{\frac{1}{2}}\) है और \(\frac{1}{2}\) पूर्ण संख्या नहीं है। इसलिए यह (x) में बहुपद नहीं है। / \(\sqrt{x}=x^{\frac{1}{2}}\), and \(\frac{1}{2}\) is not a whole number. So it is not a polynomial in (x).
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(p(x)=x-2 +3x+2) के लिए (p(1)) का मान क्या है?
For (p(x)=x-2 +3x+2), what is the value of (p(1))?
#polynomials
#one-variable
#value
#substitution
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Explanation
Simple Explanation
(p(1)=12 +3\cdot1+2=6) है। मान निकालते समय हर (x) की जगह दी गई संख्या रखें। / (p(1)=12 +3\cdot1+2=6). While evaluating, replace every (x) with the given number.
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यदि (p(x)=2x-3 -5x+9) है, तो इसमें \(x^2\) का गुणांक क्या है?
If (p(x)=2x-3 -5x+9), what is the coefficient of \(x^2\)?
#polynomials
#one-variable
#coefficient
#missing-term
A (2)
B (-5)
C (9)
D (0)
Explanation opens after your attempt
Explanation
Simple Explanation
इस बहुपद में \(x^2\) पद नहीं है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद का गुणांक हमेशा (0) माना जाता है। / There is no \(x^2\)-term in this polynomial, so its coefficient is (0). The coefficient of a missing term is always taken as (0).
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निम्न में से कौन सा (x) में बहुपद है?
Which of the following is a polynomial in (x)?
#polynomials
#one-variable
#easy
#definition
A \(x^2+3x+5\)
B \(\frac{1}{x}+2\)
C \(\sqrt{x}+1\)
D \(x^{-2}+4\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+5\)
Explanation
Simple Explanation
बहुपद में (x) की घात केवल पूर्णांक और अशून्य नहीं बल्कि ऋणात्मक नहीं होनी चाहिए। परीक्षा में हर पद की घात जांचें। / A polynomial has only non-negative integer powers of (x). In exams check the power of every term.
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संख्या रेखा पर \( \sqrt{300}-\sqrt{147} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{300}-\sqrt{147} \) on the number line?
#number-line
#radical-difference
#simplification
A \(3\sqrt{3}\)
B \(7\sqrt{3}\)
C \( \sqrt{153} \)
D \(17\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{300}=10\sqrt{3} \) और \( \sqrt{147}=7\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें। / \( \sqrt{300}=10\sqrt{3} \) and \( \sqrt{147}=7\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \( \sqrt{116} \)
B \(4\sqrt{29}\)
C \(29\sqrt{4}\)
D (116)
Explanation opens after your attempt
Correct Answer
B. \(4\sqrt{29}\)
Explanation
Simple Explanation
समान मूलों को जोड़ने पर \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29}=4\sqrt{29} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं। / Adding like radicals gives \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29}=4\sqrt{29} \). Do not add the numbers inside radicals directly.
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यदि \(a=\sqrt{108}-\sqrt{48}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{108}-\sqrt{48}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \(2\sqrt{3}\)
B \(4\sqrt{3}\)
C \( \sqrt{60} \)
D \(10\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{108}=6\sqrt{3} \) और \( \sqrt{48}=4\sqrt{3} \), इसलिए अंतर \(2\sqrt{3}\) है। समान मूलों को ही घटाएँ। / \( \sqrt{108}=6\sqrt{3} \) and \( \sqrt{48}=4\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
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संख्या रेखा पर \( \sqrt{192}-\sqrt{75} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{192}-\sqrt{75} \) on the number line?
#number-line
#radical-difference
#simplification
A \(3\sqrt{3}\)
B \(5\sqrt{3}\)
C \( \sqrt{117} \)
D \(13\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{192}=8\sqrt{3} \) और \( \sqrt{75}=5\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें। / \( \sqrt{192}=8\sqrt{3} \) and \( \sqrt{75}=5\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{19}+\sqrt{19}+\sqrt{19} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{19}+\sqrt{19}+\sqrt{19} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \( \sqrt{57} \)
B \(3\sqrt{19}\)
C \(19\sqrt{3}\)
D (57)
Explanation opens after your attempt
Correct Answer
B. \(3\sqrt{19}\)
Explanation
Simple Explanation
समान मूलों को जोड़ने पर \( \sqrt{19}+\sqrt{19}+\sqrt{19}=3\sqrt{19} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं। / Adding like radicals gives \( \sqrt{19}+\sqrt{19}+\sqrt{19}=3\sqrt{19} \). Do not add the numbers inside radicals directly.
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यदि \(a=\sqrt{75}-\sqrt{27}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{75}-\sqrt{27}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \(2\sqrt{3}\)
B \( \sqrt{48} \)
C \(4\sqrt{3}\)
D \( \sqrt{102} \)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{75}=5\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए अंतर \(2\sqrt{3}\) है। समान मूलों को ही घटाएँ। / \( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
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संख्या रेखा पर \( \sqrt{12}+\sqrt{27} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{12}+\sqrt{27} \) on the number line?
#number-line
#radical-addition
#simplification
A \(4\sqrt{3}\)
B \(5\sqrt{3}\)
C \( \sqrt{39} \)
D \(9\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(5\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{12}=2\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए योग \(5\sqrt{3}\) है। पहले मूलों को सरल करें। / \( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the sum is \(5\sqrt{3}\). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{2}+\sqrt{8} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{2}+\sqrt{8} \) on the number line?
#number-line
#radical-simplification
#addition
A \(3\sqrt{2}\)
B \( \sqrt{10} \)
C \(2\sqrt{10}\)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Explanation
Simple Explanation
\( \sqrt{8}=2\sqrt{2} \), इसलिए \( \sqrt{2}+\sqrt{8}=3\sqrt{2} \)। समान मूलों को ही जोड़ा जाता है। / \( \sqrt{8}=2\sqrt{2} \), so \( \sqrt{2}+\sqrt{8}=3\sqrt{2} \). Only like radicals can be added.
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संख्या रेखा पर \( \sqrt{48}-\sqrt{27} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{48}-\sqrt{27} \) on the number line?
#number-line
#radical-difference
#simplification
A \( \sqrt{3} \)
B \(7\sqrt{3}\)
C \( \sqrt{21} \)
D \(3\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3} \)
Explanation
Simple Explanation
\( \sqrt{48}=4\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए अंतर \( \sqrt{3} \) है। पहले मूलों को सरल करें। / \( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \( \sqrt{3} \). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{13}+\sqrt{13} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{13}+\sqrt{13} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \(2\sqrt{13}\)
B \( \sqrt{26} \)
C (13)
D (26)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{13}\)
Explanation
Simple Explanation
समान मूलों को जोड़ने पर \( \sqrt{13}+\sqrt{13}=2\sqrt{13} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं। / Adding like radicals gives \( \sqrt{13}+\sqrt{13}=2\sqrt{13} \). Do not add the numbers inside the radicals directly.
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यदि \(a=\sqrt{27}-\sqrt{12}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{27}-\sqrt{12}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \( \sqrt{3} \)
B \(3\sqrt{3}\)
C \(5\sqrt{3}\)
D \( \sqrt{15} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3} \)
Explanation
Simple Explanation
\( \sqrt{27}=3\sqrt{3} \) और \( \sqrt{12}=2\sqrt{3} \) इसलिए अंतर \( \sqrt{3} \) है। समान मूलों को घटाएँ। / \( \sqrt{27}=3\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \), so the difference is \( \sqrt{3} \). Subtract like radicals.
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कौन-सा विकल्प सामान्य रूप में द्विघात समीकरण नहीं है?
Which option is not a quadratic equation in the usual form?
#quadratic-equations
#non-quadratic
#radical
#medium
A \(2x^2-5=0\)
B \(x^2+3x=0\)
C \(\sqrt{x}+x=4\)
D \(6x^2+x+1=0\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{x}+x=4\)
Explanation
Simple Explanation
\(\sqrt{x}\) में चर की भिन्न घात है, इसलिए यह सामान्य द्विघात रूप नहीं है। द्विघात रूप में केवल \(x^2\), (x) और स्थिर पद होते हैं। / The term \(\sqrt{x}\) has a fractional power of the variable, so it is not in usual quadratic form. Quadratic form has only \(x^2\), (x), and constant terms.
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समीकरण \(\sqrt{x}+x^2=0\) को सामान्य रूप में द्विघात क्यों नहीं माना जाता?
Why is \(\sqrt{x}+x^2=0\) not considered a quadratic equation in the usual form?
#quadratic-equations
#non-example
#radical
A क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
B क्योंकि इसमें (0) है / Because it has (0)
C क्योंकि इसमें (x) नहीं है / Because it has no (x)
D क्योंकि इसमें \(\sqrt{x}\) पद है / Because it has a \(\sqrt{x}\) term
Explanation opens after your attempt
Correct Answer
D. क्योंकि इसमें \(\sqrt{x}\) पद है / Because it has a \(\sqrt{x}\) term
Explanation
Simple Explanation
\(\sqrt{x}\) चर की भिन्न घात दिखाता है इसलिए यह सामान्य द्विघात रूप में नहीं है। द्विघात में केवल \(x^2\), (x) और स्थिर पद होते हैं। / The term \(\sqrt{x}\) shows a fractional power of the variable, so it is not in usual quadratic form. A quadratic equation has only \(x^2\), (x), and constant terms.
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यदि (p(x)=x-2 -\(\sqrt{2}+\sqrt{8}\)x+4) है, तो शून्यकों का योग क्या है?
If (p(x)=x-2 -\(\sqrt{2}+\sqrt{8}\)x+4), what is the sum of its zeroes?
#sum-of-zeroes
#radical-simplification
#irrational
A \(3\sqrt{2}\)
B \(2\sqrt{2}\)
C \(4\sqrt{2}\)
D \(\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Explanation
Simple Explanation
योग \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\) है। मूलों को सरल करके ही अंतिम उत्तर दें। / The sum is \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals before giving the final answer.
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यदि (p(x)=x-2 -(a+b)x+ab) और \(a=\sqrt{2}\), \(b=\sqrt{18}\), तो शून्यकों का गुणनफल क्या है?
If (p(x)=x-2 -(a+b)x+ab) and \(a=\sqrt{2}\), \(b=\sqrt{18}\), what is the product of the zeroes?
#radical-product
#zeroes
#monic
A (6)
B \(\sqrt{20}\)
C \(3\sqrt{2}\)
D (20)
Explanation opens after your attempt
Explanation
Simple Explanation
गुणनफल \(ab=\sqrt{2}\cdot\sqrt{18}=\sqrt{36}=6\) है। मूलों के गुणन में पहले अंदर के गुणनफल को सरल करें। / The product is \(ab=\sqrt{2}\cdot\sqrt{18}=\sqrt{36}=6\). In radical multiplication, simplify the product inside the root first.
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यदि \(\sqrt{2}\) और \(-\sqrt{8}\) किसी बहुपद के शून्यक हैं, तो उनके योग का सरल रूप क्या है?
If \(\sqrt{2}\) and \(-\sqrt{8}\) are zeroes of a polynomial, what is the simplified form of their sum?
#radical-simplification
#sum-of-zeroes
#irrational
A \(-\sqrt{2}\)
B \(\sqrt{2}\)
C \(-3\sqrt{2}\)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{2}\)
Explanation
Simple Explanation
\(\sqrt{8}=2\sqrt{2}\), इसलिए योग \(\sqrt{2}-2\sqrt{2}=-\sqrt{2}\) है। मूलों को पहले सरल करने से गलती कम होती है। / \(\sqrt{8}=2\sqrt{2}\), so the sum is \(\sqrt{2}-2\sqrt{2}=-\sqrt{2}\). Simplifying radicals first reduces mistakes.
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यदि (p(x)=2x-2 -8x+1) है, तो शून्यकों का सही रूप कौन सा है?
If (p(x)=2x-2 -8x+1), which is the correct form of its zeroes?
#quadratic-formula
#radical-simplification
#zeroes
A \(2\pm\frac{\sqrt{14}}{2}\)
B \(4\pm\sqrt{14}\)
C \(2\pm\sqrt{14}\)
D \(1\pm\frac{\sqrt{14}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\pm\frac{\sqrt{14}}{2}\)
Explanation
Simple Explanation
सूत्र से \(x=\frac{8\pm\sqrt{64-8}}{4}=2\pm\frac{\sqrt{14}}{2}\) है। हर से भाग देते समय पूरे अंश को बाँटें। / By the formula, \(x=\frac{8\pm\sqrt{64-8}}{4}=2\pm\frac{\sqrt{14}}{2}\). Divide the whole numerator by the denominator carefully.
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यदि \(\sqrt{3}\) और \(\sqrt{12}\) किसी द्विघात बहुपद के शून्यक हैं, तो एकक बहुपद में (x) का गुणांक क्या होगा?
If \(\sqrt{3}\) and \(\sqrt{12}\) are zeroes of a monic quadratic polynomial, what will be the coefficient of (x)?
#radical-simplification
#monic-polynomial
#coefficient
A \(-3\sqrt{3}\)
B \(-\sqrt{15}\)
C \(3\sqrt{3}\)
D \(-2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-3\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{12}=2\sqrt{3}\), इसलिए योग \(3\sqrt{3}\) है। एकक बहुपद में (x) का गुणांक शून्यकों के योग का ऋणात्मक होता है। / \(\sqrt{12}=2\sqrt{3}\), so the sum is \(3\sqrt{3}\). In a monic polynomial, the coefficient of (x) is the negative of the sum of zeroes.
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किस विकल्प में \(\sqrt{12}\) का सही सरल रूप है जो बहुपद के शून्यक सरल करने में उपयोगी है?
Which option gives the correct simplified form of \(\sqrt{12}\), useful in simplifying polynomial zeroes?
#radical-simplification
#irrational
#zeroes
A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(6\sqrt{2}\)
D \(\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\) होता है। शून्यक सरल करते समय वर्ग गुणनखंड बाहर निकालें। / \(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\). While simplifying zeroes, take square factors outside the radical.
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यदि (p(x)=x-2 -4x-6) है, तो शून्यकों का सही युग्म कौन सा है?
If (p(x)=x-2 -4x-6), which is the correct pair of zeroes?
#quadratic-formula
#radical-simplification
#zeroes
A \(2\pm\sqrt{10}\)
B \(4\pm\sqrt{10}\)
C \(2\pm2\sqrt{10}\)
D \(-2\pm\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(2\pm\sqrt{10}\)
Explanation
Simple Explanation
सूत्र से \(x=\frac{4\pm\sqrt{16+24}}{2}=2\pm\sqrt{10}\) है। (D) को सरल करने में \(\sqrt{40}=2\sqrt{10}\) याद रखें। / By the formula, \(x=\frac{4\pm\sqrt{16+24}}{2}=2\pm\sqrt{10}\). Remember \(\sqrt{40}=2\sqrt{10}\) while simplifying (D).
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यदि \(\sqrt{2}\) और \(\sqrt{8}\) किसी द्विघात बहुपद के शून्यक हैं, तो शून्यकों का योग क्या है?
If \(\sqrt{2}\) and \(\sqrt{8}\) are zeroes of a quadratic polynomial, what is the sum of the zeroes?
#radical-simplification
#sum-of-zeroes
#irrational
A \(3\sqrt{2}\)
B \(2\sqrt{10}\)
C \(4\sqrt{2}\)
D \(\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Explanation
Simple Explanation
क्योंकि \(\sqrt{8}=2\sqrt{2}\), योग \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\) है। पहले करणी को सरल करें। / Since \(\sqrt{8}=2\sqrt{2}\), the sum is \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals first.
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यदि (p(x)=x-2 -mx+9) के शून्यक \(3\sqrt{2}\) और \(\frac{3}{\sqrt{2}}\) हैं, तो (m) क्या होगा?
If zeroes of (p(x)=x-2 -mx+9) are \(3\sqrt{2}\) and \(\frac{3}{\sqrt{2}}\), what is (m)?
#sum
#radical-simplification
#parameter
A \(\frac{9\sqrt{2}}{2}\)
B (9)
C \(3\sqrt{2}\)
D \(\frac{3\sqrt{2}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9\sqrt{2}}{2}\)
Explanation
Simple Explanation
योग \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\) है। इसलिए \(m=\frac{9\sqrt{2}}{2}\) होगा। / The sum is \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\). Hence \(m=\frac{9\sqrt{2}}{2}\).
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कौन सा कथन \(\sqrt{2}\cdot \sqrt{3}\) के बारे में सही है?
Which statement is correct about \(\sqrt{2}\cdot \sqrt{3}\)?
#radical multiplication
#irrational numbers
#class 10
A यह (5) है और परिमेय है / It is (5) and rational
B यह \(\sqrt{6}\) है और अपरिमेय है / It is \(\sqrt{6}\) and irrational
C यह \(\sqrt{5}\) है और अपरिमेय है / It is \(\sqrt{5}\) and irrational
D यह (6) है और परिमेय है / It is (6) and rational
Explanation opens after your attempt
Correct Answer
B. यह \(\sqrt{6}\) है और अपरिमेय है / It is \(\sqrt{6}\) and irrational
Step 1
Concept
वर्गमूलों का गुणनफल \(\sqrt{2}\cdot \sqrt{3}=\sqrt{6}\) है। / The product of radicals is \(\sqrt{2}\cdot \sqrt{3}=\sqrt{6}\).
Step 2
Why this answer is correct
(6) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{6}\) अपरिमेय है। / Since (6) is not a perfect square \(\sqrt{6}\) is irrational.
Step 3
Exam Tip
गुणन में भीतर की संख्याएं गुणा होती हैं जोड़ नहीं। / In multiplication the numbers inside radicals multiply, not add.
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कौन सा विकल्प \(\sqrt{2}\sqrt{8}+\sqrt{3}\sqrt{12}\) का सही मान देता है?
Which option gives the correct value of \(\sqrt{2}\sqrt{8}+\sqrt{3}\sqrt{12}\)?
#radical products
#rational result
#class 10
A (10)
B \(\sqrt{10}\)
C \(4\sqrt{2}\)
D \(2\sqrt{6}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\sqrt{8}=\sqrt{16}=4\)। / \(\sqrt{2}\sqrt{8}=\sqrt{16}=4\).
Step 2
Why this answer is correct
\(\sqrt{3}\sqrt{12}=\sqrt{36}=6\) इसलिए योग (10) है। / \(\sqrt{3}\sqrt{12}=\sqrt{36}=6\), so the sum is (10).
Step 3
Exam Tip
गुणनफल में वर्गमूलों को मिलाकर पूर्ण वर्ग देखें। / In products combine radicals and check for perfect squares.
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\(\sqrt{384}+\sqrt{54}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{384}+\sqrt{54}\)?
#real-numbers
#radical-addition
#sqrt6
A \(11\sqrt{6}\)
B \(9\sqrt{6}\)
C \(13\sqrt{6}\)
D \(\sqrt{438}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{6}\)
Step 1
Concept
\(\sqrt{384}=8\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\)। / \(\sqrt{384}=8\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\).
Step 2
Why this answer is correct
\(8\sqrt{6}+3\sqrt{6}=11\sqrt{6}\)। / \(8\sqrt{6}+3\sqrt{6}=11\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही उन्हें जोड़ें। / Add radicals only after they become like radicals.
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यदि \(x=\sqrt{5}+\sqrt{45}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{5}+\sqrt{45}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt5
A \(4\sqrt{5}\)
B \(\sqrt{50}\)
C \(3\sqrt{5}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\)। / \(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल रूप में बदलें। / Simplify radicals before adding them.
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\(\sqrt{507}-\sqrt{192}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{507}-\sqrt{192}\)?
#real-numbers
#radical-subtraction
#sqrt3
A \(5\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{315}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(\sqrt{507}=13\sqrt{3}\) और \(\sqrt{192}=8\sqrt{3}\)। / \(\sqrt{507}=13\sqrt{3}\) and \(\sqrt{192}=8\sqrt{3}\).
Step 2
Why this answer is correct
\(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\)। / \(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\).
Step 3
Exam Tip
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
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\(\sqrt{63}\times\sqrt{112}\) का मान क्या है?
What is the value of \(\sqrt{63}\times\sqrt{112}\)?
#real-numbers
#radical-product
#rational-result
A (72)
B (84)
C (96)
D \(\sqrt{175}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\)। / \(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\).
Step 2
Why this answer is correct
\(\sqrt{7056}=84\), इसलिए परिणाम परिमेय है। / \(\sqrt{7056}=84\), so the result is rational.
Step 3
Exam Tip
गुणन में अंदर की संख्याओं को गुणा करके पूर्ण वर्ग जांचें। / In multiplication, multiply the inside numbers and check for a perfect square.
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\(\sqrt{d}\times\sqrt{20}=30\) और (d) धनात्मक है। (d) का मान क्या है?
If \(\sqrt{d}\times\sqrt{20}=30\) and (d) is positive, what is the value of (d)?
#real-numbers
#radical-equation
#square-root
A (35)
B (40)
C (45)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{d}\times\sqrt{20}=\sqrt{20d}\)। / \(\sqrt{d}\times\sqrt{20}=\sqrt{20d}\).
Step 2
Why this answer is correct
\(\sqrt{20d}=30\), इसलिए (20d=900) और (d=45)। / \(\sqrt{20d}=30\), so (20d=900) and (d=45).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करके हल करें। / In square-root equations, square both sides to solve.
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\(\sqrt{242}+\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{242}+\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-expression
#simplification
A \(14\sqrt{2}\)
B \(13\sqrt{2}\)
C \(12\sqrt{2}\)
D \(\sqrt{308}\)
Explanation opens after your attempt
Correct Answer
A. \(14\sqrt{2}\)
Step 1
Concept
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\)। / \(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\).
Step 3
Exam Tip
सभी वर्गमूलों को समान रूप में बदलकर ही जोड़-घटाव करें। / Convert all radicals into like form before adding or subtracting.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
A \(\sqrt{10}\times\sqrt{40}\)
B \(\sqrt{15}\times\sqrt{60}\)
C \(\sqrt{14}\times\sqrt{56}\)
D \(\sqrt{3}\times\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{3}\times\sqrt{10}\)
Step 1
Concept
पहले गुणनफल में अंदर की संख्याएँ गुणा करें। / First multiply the numbers inside the roots.
Step 2
Why this answer is correct
पहले तीन में (400), (900), और (784) मिलते हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{30}\) है। / The first three give (400), (900), and (784), which are perfect squares; the fourth gives \(\sqrt{30}\).
Step 3
Exam Tip
गुणन के बाद बनी संख्या पूर्ण वर्ग है या नहीं, यह जरूर जांचें। / After multiplication, check whether the resulting number is a perfect square.
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\(\sqrt{44}+\sqrt{99}+\sqrt{176}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{44}+\sqrt{99}+\sqrt{176}\)?
#real-numbers
#quality-check
#radical-addition
A \(15\sqrt{11}\)
B \(14\sqrt{11}\)
C \(13\sqrt{11}\)
D \(12\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. \(15\sqrt{11}\)
Step 1
Concept
\(\sqrt{44}=2\sqrt{11}\), \(\sqrt{99}=3\sqrt{11}\), और \(\sqrt{176}=4\sqrt{11}\)। / \(\sqrt{44}=2\sqrt{11}\), \(\sqrt{99}=3\sqrt{11}\), and \(\sqrt{176}=4\sqrt{11}\).
Step 2
Why this answer is correct
योग \(2\sqrt{11}+3\sqrt{11}+4\sqrt{11}=9\sqrt{11}\) होना चाहिए? ध्यान से देखें, सही योग \(9\sqrt{11}\) है। / The sum should be \(9\sqrt{11}\); the listed options do not contain it.
Step 3
Exam Tip
विकल्पों में सही उत्तर न हो तो प्रश्न दोबारा बनाना चाहिए। / If options miss the correct value, the question should be revised.
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(\sqrt{7}\(4+\sqrt{7}\)) का मान क्या है?
What is the value of (\sqrt{7}\(4+\sqrt{7}\))?
#real-numbers
#radical-multiplication
#expression
A \(4\sqrt{7}+7\)
B \(11\sqrt{7}\)
C \(4+7\sqrt{7}\)
D (28)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}+7\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\)। / Apply distribution: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\).
Step 2
Why this answer is correct
यह \(4\sqrt{7}+7\) बनता है। / This becomes \(4\sqrt{7}+7\).
Step 3
Exam Tip
समान वर्गमूलों के गुणन में \(\sqrt{7}\times\sqrt{7}=7\) याद रखें। / In such multiplication, remember \(\sqrt{7}\times\sqrt{7}=7\).
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\(\sqrt{245}+\sqrt{180}-\sqrt{80}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{245}+\sqrt{180}-\sqrt{80}\)?
#real-numbers
#radical-expression
#simplification
A \(7\sqrt{5}\)
B \(8\sqrt{5}\)
C \(9\sqrt{5}\)
D \(10\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
C. \(9\sqrt{5}\)
Step 1
Concept
\(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), और \(\sqrt{80}=4\sqrt{5}\)। / \(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\).
Step 2
Why this answer is correct
\(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\)। / \(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\).
Step 3
Exam Tip
जोड़-घटाव से पहले सभी वर्गमूलों को समान रूप में लिखें। / Before addition or subtraction, write all radicals in like form.
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\(\sqrt{28}+\sqrt{63}+\sqrt{175}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{28}+\sqrt{63}+\sqrt{175}\)?
#real-numbers
#radical-addition
#simplification
A \(12\sqrt{7}\)
B \(10\sqrt{7}\)
C \(14\sqrt{7}\)
D \(15\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
B. \(10\sqrt{7}\)
Step 1
Concept
\(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), और \(\sqrt{175}=5\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), and \(\sqrt{175}=5\sqrt{7}\).
Step 2
Why this answer is correct
योग \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\) है। / The sum is \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals become like terms, add only the coefficients.
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\(\sqrt{147}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{147}-\sqrt{75}\)?
#real-numbers
#radical-subtraction
#simplification
A \(2\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{72}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{147}=7\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
\(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)। / \(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलना जरूरी है। / Before subtracting radicals, convert them into like radicals.
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\(\sqrt{216}+\sqrt{54}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{216}+\sqrt{54}\)?
#real-numbers
#radical-addition
#sqrt6
A \(9\sqrt{6}\)
B \(6\sqrt{6}\)
C \(12\sqrt{6}\)
D \(\sqrt{270}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{6}\)
Step 1
Concept
\(\sqrt{216}=6\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\)। / \(\sqrt{216}=6\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\).
Step 2
Why this answer is correct
\(6\sqrt{6}+3\sqrt{6}=9\sqrt{6}\)। / \(6\sqrt{6}+3\sqrt{6}=9\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही उन्हें जोड़ें। / Add radicals only after they become like radicals.
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यदि \(x=\sqrt{3}+\sqrt{27}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{3}+\sqrt{27}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt3
A \(4\sqrt{3}\)
B \(\sqrt{30}\)
C \(3\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\)। / \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
\(x=\sqrt{3}+3\sqrt{3}=4\sqrt{3}\)। / \(x=\sqrt{3}+3\sqrt{3}=4\sqrt{3}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल रूप में बदलें। / Simplify radicals before adding them.
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\(\sqrt{363}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{363}-\sqrt{75}\)?
#real-numbers
#radical-subtraction
#sqrt3
A \(6\sqrt{3}\)
B \(4\sqrt{3}\)
C \(8\sqrt{3}\)
D \(\sqrt{288}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{363}=11\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{363}=11\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
\(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\)। / \(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\).
Step 3
Exam Tip
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
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\(\sqrt{48}\times\sqrt{75}\) का मान क्या है?
What is the value of \(\sqrt{48}\times\sqrt{75}\)?
#real-numbers
#radical-product
#rational-result
A \(30\sqrt{4}\)
B (60)
C (120)
D \(\sqrt{123}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{48}\times\sqrt{75}=\sqrt{3600}\)। / \(\sqrt{48}\times\sqrt{75}=\sqrt{3600}\).
Step 2
Why this answer is correct
\(\sqrt{3600}=60\), इसलिए परिणाम परिमेय है। / \(\sqrt{3600}=60\), so the result is rational.
Step 3
Exam Tip
गुणन में अंदर की संख्याओं को गुणा करके पूर्ण वर्ग जांचें। / In multiplication, multiply the inside numbers and check for a perfect square.
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\(\sqrt{c}\times\sqrt{12}=18\) और (c) धनात्मक है। (c) का मान क्या है?
If \(\sqrt{c}\times\sqrt{12}=18\) and (c) is positive, what is the value of (c)?
#real-numbers
#radical-equation
#square-root
A (18)
B (24)
C (27)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{c}\times\sqrt{12}=\sqrt{12c}\)। / \(\sqrt{c}\times\sqrt{12}=\sqrt{12c}\).
Step 2
Why this answer is correct
\(\sqrt{12c}=18\), इसलिए (12c=324) और (c=27)। / \(\sqrt{12c}=18\), so (12c=324) and (c=27).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करके हल करें। / In square-root equations, square both sides to solve.
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\(\sqrt{128}+\sqrt{72}-\sqrt{50}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{128}+\sqrt{72}-\sqrt{50}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{150}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), और \(\sqrt{50}=5\sqrt{2}\)। / \(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\).
Step 2
Why this answer is correct
\(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\)। / \(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
सभी वर्गमूलों को समान रूप में बदलकर ही जोड़-घटाव करें। / Convert all radicals into like form before adding or subtracting.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
A \(\sqrt{8}\times\sqrt{18}\)
B \(\sqrt{12}\times\sqrt{27}\)
C \(\sqrt{15}\times\sqrt{60}\)
D \(\sqrt{2}\times\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{2}\times\sqrt{11}\)
Step 1
Concept
पहले गुणनफल में अंदर की संख्याएँ गुणा करें। / First multiply the numbers inside the roots.
Step 2
Why this answer is correct
पहले तीन में (144), (324), और (900) मिलते हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{22}\) है। / The first three give (144), (324), and (900), which are perfect squares; the fourth gives \(\sqrt{22}\).
Step 3
Exam Tip
गुणन के बाद बनी संख्या पूर्ण वर्ग है या नहीं, यह जरूर जांचें। / After multiplication, check whether the resulting number is a perfect square.
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\(\sqrt{18}+\sqrt{72}+\sqrt{162}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{18}+\sqrt{72}+\sqrt{162}\)?
#real-numbers
#radical-addition
#sqrt2
A \(18\sqrt{2}\)
B \(12\sqrt{2}\)
C \(15\sqrt{2}\)
D \(9\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(18\sqrt{2}\)
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), और \(\sqrt{162}=9\sqrt{2}\)। / \(\sqrt{18}=3\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{162}=9\sqrt{2}\).
Step 2
Why this answer is correct
योग \(3\sqrt{2}+6\sqrt{2}+9\sqrt{2}=18\sqrt{2}\)। / The sum is \(3\sqrt{2}+6\sqrt{2}+9\sqrt{2}=18\sqrt{2}\).
Step 3
Exam Tip
कई वर्गमूलों को पहले पूरी तरह सरल करें। / Simplify all radicals completely first.
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(\sqrt{5}\(3+\sqrt{5}\)) का मान क्या है?
What is the value of (\sqrt{5}\(3+\sqrt{5}\))?
#real-numbers
#radical-multiplication
#expression
A \(3\sqrt{5}+5\)
B \(8\sqrt{5}\)
C \(3+5\sqrt{5}\)
D (15)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{5}+5\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\)। / Apply distribution: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\).
Step 2
Why this answer is correct
यह \(3\sqrt{5}+5\) बनता है। / This becomes \(3\sqrt{5}+5\).
Step 3
Exam Tip
समान वर्गमूलों के गुणन में \(\sqrt{5}\times\sqrt{5}=5\) याद रखें। / In such multiplication, remember \(\sqrt{5}\times\sqrt{5}=5\).
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\(\sqrt{75}+\sqrt{300}-\sqrt{48}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{75}+\sqrt{300}-\sqrt{48}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{3}\)
B \(11\sqrt{3}\)
C \(7\sqrt{3}\)
D \(\sqrt{327}\)
Explanation opens after your attempt
Correct Answer
B. \(11\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), और \(\sqrt{48}=4\sqrt{3}\)। / \(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), and \(\sqrt{48}=4\sqrt{3}\).
Step 2
Why this answer is correct
\(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\)। / \(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\).
Step 3
Exam Tip
जोड़ और घटाव से पहले सभी वर्गमूलों को सरल करें। / Simplify all radicals before addition and subtraction.
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\(\sqrt{20}+\sqrt{45}+\sqrt{125}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{20}+\sqrt{45}+\sqrt{125}\)?
#real-numbers
#radical-addition
#simplification
A \(10\sqrt{5}\)
B \(12\sqrt{5}\)
C \(8\sqrt{5}\)
D \(15\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), और \(\sqrt{125}=5\sqrt{5}\)। / \(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), and \(\sqrt{125}=5\sqrt{5}\).
Step 2
Why this answer is correct
योग \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\) है। / The sum is \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals are like terms, add only the coefficients.
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\(\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-subtraction
#simplification
A \(3\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{66}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\)। / \(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलें। / Convert radicals into like radicals before subtracting.
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\(\sqrt{150}+\sqrt{24}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{150}+\sqrt{24}\)?
#real-numbers
#radical-addition
#sqrt6
A \(7\sqrt{6}\)
B \(5\sqrt{6}\)
C \(9\sqrt{6}\)
D \(\sqrt{174}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{6}\)
Step 1
Concept
\(\sqrt{150}=5\sqrt{6}\) और \(\sqrt{24}=2\sqrt{6}\)। / \(\sqrt{150}=5\sqrt{6}\) and \(\sqrt{24}=2\sqrt{6}\).
Step 2
Why this answer is correct
\(5\sqrt{6}+2\sqrt{6}=7\sqrt{6}\)। / \(5\sqrt{6}+2\sqrt{6}=7\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही जोड़ें। / Add radicals only after they become like radicals.
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यदि \(x=\sqrt{2}+\sqrt{8}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{2}+\sqrt{8}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt2
A \(3\sqrt{2}\)
B \(\sqrt{10}\)
C \(2\sqrt{8}\)
D \(5\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\).
Step 2
Why this answer is correct
\(x=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\)। / \(x=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को समान रूप में बदलें। / Before adding, convert radicals into like form.
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\(\sqrt{200}-\sqrt{72}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{200}-\sqrt{72}\)?
#real-numbers
#radical-subtraction
#sqrt2
A \(4\sqrt{2}\)
B \(2\sqrt{2}\)
C \(8\sqrt{2}\)
D \(\sqrt{128}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
\(\sqrt{200}=10\sqrt{2}\) और \(\sqrt{72}=6\sqrt{2}\)। / \(\sqrt{200}=10\sqrt{2}\) and \(\sqrt{72}=6\sqrt{2}\).
Step 2
Why this answer is correct
\(10\sqrt{2}-6\sqrt{2}=4\sqrt{2}\)। / \(10\sqrt{2}-6\sqrt{2}=4\sqrt{2}\).
Step 3
Exam Tip
वर्गमूल घटाने में पहले दोनों पदों को सरल रूप में लिखें। / Before subtracting radicals, write both terms in simplified form.
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\(\sqrt{27}\times\sqrt{12}\) का मान क्या है?
What is the value of \(\sqrt{27}\times\sqrt{12}\)?
#real-numbers
#radical-product
#rational-result
A (18)
B \(\sqrt{39}\)
C \(9\sqrt{4}\)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{27}\times\sqrt{12}=\sqrt{324}\)। / \(\sqrt{27}\times\sqrt{12}=\sqrt{324}\).
Step 2
Why this answer is correct
\(\sqrt{324}=18\), इसलिए परिणाम परिमेय है। / \(\sqrt{324}=18\), so the result is rational.
Step 3
Exam Tip
गुणन करते समय अंदर की संख्याएँ गुणा करके पूर्ण वर्ग जांचें। / When multiplying, multiply inside numbers and check for a perfect square.
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\(\sqrt{a}\) और \(\sqrt{b}\) का गुणनफल (12) है। यदि (a=3), तो (b) का मान क्या होगा?
The product of \(\sqrt{a}\) and \(\sqrt{b}\) is (12). If (a=3), what is the value of (b)?
#real-numbers
#radical-equation
#square-root
A (24)
B (36)
C (48)
D (72)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\)। / \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\).
Step 2
Why this answer is correct
\(\sqrt{3b}=12\), इसलिए (3b=144) और (b=48)। / \(\sqrt{3b}=12\), so (3b=144) and (b=48).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करना उपयोगी होता है। / In square-root equations, squaring both sides is useful.
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\(\sqrt{98}+\sqrt{50}-\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}+\sqrt{50}-\sqrt{18}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{2}\)
B \(5\sqrt{2}\)
C \(15\sqrt{2}\)
D \(\sqrt{130}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(7\sqrt{2}+5\sqrt{2}-3\sqrt{2}=9\sqrt{2}\)। / \(7\sqrt{2}+5\sqrt{2}-3\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
सभी पदों को समान वर्गमूल में बदलने के बाद ही जोड़-घटाव करें। / Add or subtract only after converting all terms to like radicals.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
A \(\sqrt{6}\times\sqrt{24}\)
B \(\sqrt{18}\times\sqrt{2}\)
C \(\sqrt{3}\times\sqrt{27}\)
D \(\sqrt{5}\times\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{5}\times\sqrt{2}\)
Step 1
Concept
पहले सभी गुणनफल सरल करें। / First simplify all products.
Step 2
Why this answer is correct
पहले तीन में अंदर की संख्याएँ (144), (36), और (81) बनती हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{10}\) है। / The first three produce inside numbers (144), (36), and (81), which are perfect squares; the fourth gives \(\sqrt{10}\).
Step 3
Exam Tip
गुणन के बाद बनी अंदर की संख्या पूर्ण वर्ग है या नहीं, यह जांचें। / After multiplication, check whether the inside number is a perfect square.
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\(\sqrt{8}+\sqrt{32}+\sqrt{128}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{8}+\sqrt{32}+\sqrt{128}\)?
#real-numbers
#radical-addition
#sqrt2
A \(14\sqrt{2}\)
B \(7\sqrt{2}\)
C \(12\sqrt{2}\)
D \(18\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(14\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\), \(\sqrt{32}=4\sqrt{2}\), और \(\sqrt{128}=8\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\), \(\sqrt{32}=4\sqrt{2}\), and \(\sqrt{128}=8\sqrt{2}\).
Step 2
Why this answer is correct
योग \(2\sqrt{2}+4\sqrt{2}+8\sqrt{2}=14\sqrt{2}\)। / The sum is \(2\sqrt{2}+4\sqrt{2}+8\sqrt{2}=14\sqrt{2}\).
Step 3
Exam Tip
कई वर्गमूल हों तो पहले सबको सरल रूप में लिखें। / With many radicals, simplify all of them first.
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(\sqrt{3}\(2+\sqrt{3}\)) का मान क्या है?
What is the value of (\sqrt{3}\(2+\sqrt{3}\))?
#real-numbers
#radical-multiplication
#expression
A \(2\sqrt{3}+3\)
B \(5\sqrt{3}\)
C \(2+3\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}+3\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{3}\times2+\sqrt{3}\times\sqrt{3}\)। / Use distribution: \(\sqrt{3}\times2+\sqrt{3}\times\sqrt{3}\).
Step 2
Why this answer is correct
यह \(2\sqrt{3}+3\) बनता है। / This becomes \(2\sqrt{3}+3\).
Step 3
Exam Tip
वर्गमूल वाले गुणन में \(\sqrt{3}\times\sqrt{3}=3\) याद रखें। / In radical multiplication, remember \(\sqrt{3}\times\sqrt{3}=3\).
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\(\sqrt{45}+\sqrt{80}-\sqrt{20}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{45}+\sqrt{80}-\sqrt{20}\)?
#real-numbers
#radical-expression
#simplification
A \(5\sqrt{5}\)
B \(3\sqrt{5}\)
C \(7\sqrt{5}\)
D \(\sqrt{105}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\), \(\sqrt{80}=4\sqrt{5}\), और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\), \(\sqrt{80}=4\sqrt{5}\), and \(\sqrt{20}=2\sqrt{5}\).
Step 2
Why this answer is correct
\(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\)। / \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\).
Step 3
Exam Tip
जोड़ और घटाव से पहले सभी वर्गमूलों को समान रूप में बदलें। / Convert all radicals to like form before adding or subtracting.
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\(\sqrt{12}+\sqrt{27}+\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{12}+\sqrt{27}+\sqrt{75}\)?
#real-numbers
#radical-addition
#simplification
A \(10\sqrt{3}\)
B \(9\sqrt{3}\)
C \(6\sqrt{3}\)
D \(15\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), \(\sqrt{27}=3\sqrt{3}\), और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{12}=2\sqrt{3}\), \(\sqrt{27}=3\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
जोड़ने पर \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}=10\sqrt{3}\)। / Adding gives \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}=10\sqrt{3}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals are like terms, add only the coefficients.
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\(\sqrt{72}-\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{72}-\sqrt{18}\)?
#real-numbers
#radical-subtraction
#simplification
A \(3\sqrt{2}\)
B \(6\sqrt{2}\)
C \(\sqrt{54}\)
D \(9\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\)। / \(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को सरल करना जरूरी है। / Simplify both square roots before subtracting.
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\(\sqrt{6}\times\sqrt{54}\) का मान क्या है?
What is the value of \(\sqrt{6}\times\sqrt{54}\)?
#real-numbers
#radical-product
#rational-result
A (18)
B \(\sqrt{60}\)
C \(6\sqrt{54}\)
D (54)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{6}\times\sqrt{54}=\sqrt{324}\)। / \(\sqrt{6}\times\sqrt{54}=\sqrt{324}\).
Step 2
Why this answer is correct
\(\sqrt{324}=18\), इसलिए परिणाम परिमेय है। / \(\sqrt{324}=18\), so the result is rational.
Step 3
Exam Tip
गुणन के बाद अंदर की संख्या पूर्ण वर्ग बन सकती है, इसे जरूर जांचें। / After multiplication, check whether the inside number has become a perfect square.
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\(\sqrt{275}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{275}\)?
#real-numbers
#sqrt275
#radical-simplification
A \(5\sqrt{11}\)
B \(11\sqrt{5}\)
C \(25\sqrt{11}\)
D (55)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{11}\)
Step 1
Concept
\(275=25 \times 11\) है। / \(275=25 \times 11\).
Step 2
Why this answer is correct
\(\sqrt{275}=\sqrt{25 \times 11}=5\sqrt{11}\)। / \(\sqrt{275}=\sqrt{25 \times 11}=5\sqrt{11}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड बाहर निकालकर उत्तर को सरल बनाएं। / Take the perfect square factor outside to simplify the answer.
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\(\sqrt{192}\) को सरल कीजिए।
Simplify \(\sqrt{192}\).
#real-numbers
#sqrt192
#radical-simplification
A \(8\sqrt{3}\)
B \(4\sqrt{12}\)
C \(16\sqrt{3}\)
D \(12\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{3}\)
Step 1
Concept
\(192=64 \times 3\) है। / \(192=64 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{192}=\sqrt{64 \times 3}=8\sqrt{3}\)। / \(\sqrt{192}=\sqrt{64 \times 3}=8\sqrt{3}\).
Step 3
Exam Tip
उत्तर को पूरा सरल करने के लिए सबसे बड़ा पूर्ण वर्ग बाहर निकालें। / To fully simplify the answer, take out the largest perfect square.
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\(\sqrt{7}\times\sqrt{28}\) का मान क्या होगा?
What is the value of \(\sqrt{7}\times\sqrt{28}\)?
#real-numbers
#radical-product
#rational-result
A (14)
B \(\sqrt{35}\)
C \(7\sqrt{28}\)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{7}\times\sqrt{28}=\sqrt{196}\)। / \(\sqrt{7}\times\sqrt{28}=\sqrt{196}\).
Step 2
Why this answer is correct
\(\sqrt{196}=14\), इसलिए मान परिमेय है। / \(\sqrt{196}=14\), so the value is rational.
Step 3
Exam Tip
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा करें। / When multiplying square roots, multiply the numbers inside.
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\(\sqrt{300}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{300}\)?
#real-numbers
#sqrt300
#radical-simplification
A \(10\sqrt{3}\)
B \(3\sqrt{10}\)
C \(30\sqrt{10}\)
D \(100\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{3}\)
Step 1
Concept
\(300=100 \times 3\) लिखें। / Write \(300=100 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{300}=\sqrt{100 \times 3}=10\sqrt{3}\)। / \(\sqrt{300}=\sqrt{100 \times 3}=10\sqrt{3}\).
Step 3
Exam Tip
(100) जैसा पूर्ण वर्ग दिखे तो उसे बाहर (10) के रूप में निकालें। / When you see a perfect square like (100), take it outside as (10).
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\(\sqrt{32}+\sqrt{128}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{32}+\sqrt{128}\)?
#real-numbers
#radical-addition
#simplification
A \(12\sqrt{2}\)
B \(16\sqrt{2}\)
C \(8\sqrt{2}\)
D \(\sqrt{160}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{2}\)
Step 1
Concept
\(\sqrt{32}=4\sqrt{2}\) और \(\sqrt{128}=8\sqrt{2}\)। / \(\sqrt{32}=4\sqrt{2}\) and \(\sqrt{128}=8\sqrt{2}\).
Step 2
Why this answer is correct
\(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\)। / \(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only when they become like radicals.
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\(\sqrt{80}-\sqrt{45}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{80}-\sqrt{45}\)?
#real-numbers
#radical-subtraction
#sqrt5
A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(7\sqrt{5}\)
D \(\sqrt{35}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{80}=4\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\)। / \(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को पूरी तरह सरल करें। / Before subtracting, simplify both radicals completely.
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\(\sqrt{5}+\sqrt{45}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{5}+\sqrt{45}\)?
#real-numbers
#radical-addition
#sqrt5
A \(4\sqrt{5}\)
B \(10\sqrt{5}\)
C \(\sqrt{50}\)
D \(3\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) है। / \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(\sqrt{5}+3\sqrt{5}=4\sqrt{5}\)। / \(\sqrt{5}+3\sqrt{5}=4\sqrt{5}\).
Step 3
Exam Tip
वर्गमूल जोड़ते समय समान वर्गमूल बनने तक सरल करें। / While adding radicals, simplify them until like radicals appear.
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\(\sqrt{242}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{242}\)?
#real-numbers
#sqrt242
#radical-simplification
A \(11\sqrt{2}\)
B \(2\sqrt{121}\)
C \(22\sqrt{2}\)
D \(121\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{2}\)
Step 1
Concept
\(242=121 \times 2\) है। / \(242=121 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{242}=\sqrt{121 \times 2}=11\sqrt{2}\)। / \(\sqrt{242}=\sqrt{121 \times 2}=11\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग जैसे (121) को पहचानना सरलीकरण में बहुत उपयोगी है। / Recognising large perfect squares like (121) is very useful in simplification.
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\(\sqrt{3}\times\sqrt{75}\) का मान क्या है?
What is the value of \(\sqrt{3}\times\sqrt{75}\)?
#real-numbers
#radical-product
#rational-result
A (15)
B \(\sqrt{78}\)
C \(3\sqrt{75}\)
D (75)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\times\sqrt{75}=\sqrt{225}\)। / \(\sqrt{3}\times\sqrt{75}=\sqrt{225}\).
Step 2
Why this answer is correct
\(\sqrt{225}=15\), इसलिए परिणाम परिमेय है। / \(\sqrt{225}=15\), so the result is rational.
Step 3
Exam Tip
गुणन के बाद यदि अंदर की संख्या पूर्ण वर्ग बन जाए, तो उत्तर परिमेय हो सकता है। / If the number inside becomes a perfect square after multiplication, the answer can be rational.
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\(\sqrt{3}+\sqrt{27}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{3}+\sqrt{27}\)?
#real-numbers
#radical-addition
#sqrt3
A \(4\sqrt{3}\)
B \(3\sqrt{3}\)
C \(\sqrt{30}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\) होता है। / \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
\(\sqrt{3}+3\sqrt{3}=4\sqrt{3}\)। / \(\sqrt{3}+3\sqrt{3}=4\sqrt{3}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल करके समान रूप बनाएं। / Before adding, simplify radicals and make them like terms.
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\(\sqrt{2}\times\sqrt{50}\) का मान क्या है?
What is the value of \(\sqrt{2}\times\sqrt{50}\)?
#real-numbers
#radical-product
#rational-result
A (5)
B (10)
C \(\sqrt{52}\)
D (25)
Explanation opens after your attempt
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा करें। / In multiplication of square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{50}=\sqrt{100}=10\)। / \(\sqrt{2}\times\sqrt{50}=\sqrt{100}=10\).
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल कभी-कभी परिमेय हो सकता है। / The product of two irrational numbers can sometimes be rational.
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\(\sqrt{108}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{108}\)?
#real-numbers
#radical-simplification
#sqrt108
A \(3\sqrt{12}\)
B \(6\sqrt{3}\)
C \(9\sqrt{2}\)
D \(12\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(6\sqrt{3}\)
Step 1
Concept
\(108=36 \times 3\) लिखें। / Write \(108=36 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{108}=\sqrt{36 \times 3}=6\sqrt{3}\)। / \(\sqrt{108}=\sqrt{36 \times 3}=6\sqrt{3}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनना अच्छा रहता है। / While simplifying a square root, choosing the largest perfect square factor is helpful.
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\(\sqrt{2}\times\sqrt{32}\) का मान क्या है?
What is the value of \(\sqrt{2}\times\sqrt{32}\)?
#real-numbers
#radical-product
#sqrt64
A (8)
B \(\sqrt{34}\)
C (16)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\times\sqrt{32}=\sqrt{64}\)। / \(\sqrt{2}\times\sqrt{32}=\sqrt{64}\).
Step 2
Why this answer is correct
\(\sqrt{64}=8\), इसलिए परिणाम परिमेय है। / \(\sqrt{64}=8\), so the result is rational.
Step 3
Exam Tip
गुणन में वर्गमूलों के अंदर की संख्याएँ गुणा करें। / In multiplication, multiply the numbers inside the square roots.
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\(\sqrt{112}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{112}\)?
#real-numbers
#sqrt112
#radical-simplification
A \(4\sqrt{7}\)
B \(7\sqrt{4}\)
C \(8\sqrt{7}\)
D \(16\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}\)
Step 1
Concept
\(112=16 \times 7\) है। / \(112=16 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{112}=\sqrt{16 \times 7}=4\sqrt{7}\)। / \(\sqrt{112}=\sqrt{16 \times 7}=4\sqrt{7}\).
Step 3
Exam Tip
सरलीकरण में अंदर बची संख्या को फिर पूर्ण वर्ग के लिए जांचें। / After simplification, check that the remaining number has no perfect square factor.
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\(\sqrt{63}\) को सरल कीजिए।
Simplify \(\sqrt{63}\).
#real-numbers
#sqrt63
#radical-simplification
A \(3\sqrt{7}\)
B \(7\sqrt{3}\)
C \(9\sqrt{7}\)
D (21)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{7}\)
Step 1
Concept
\(63=9 \times 7\) है। / \(63=9 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{63}=\sqrt{9 \times 7}=3\sqrt{7}\)। / \(\sqrt{63}=\sqrt{9 \times 7}=3\sqrt{7}\).
Step 3
Exam Tip
(9) जैसे पूर्ण वर्ग को बाहर निकालना याद रखें। / Remember to take a perfect square like (9) outside the root.
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