निम्नलिखित में से कौन-सी संख्या अपरिमेय है?
Which of the following numbers is irrational?
#real-numbers
#irrational-numbers
#square-root
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A \(\sqrt{15}\)
B \(\sqrt{16}\)
C (0.125)
D \(\frac{7}{9}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{15}\)
Step 1
Concept
अपरिमेय संख्या को ठीक-ठीक भिन्न रूप में नहीं लिखा जा सकता। / An irrational number cannot be written exactly as a fraction.
Step 2
Why this answer is correct
(15) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{15}\) अपरिमेय है। / (15) is not a perfect square, so \(\sqrt{15}\) is irrational.
Step 3
Exam Tip
वर्गमूल वाले विकल्पों में अंदर की संख्या पूर्ण वर्ग है या नहीं, पहले यही देखें। / For square-root options, first check whether the number inside is a perfect square.
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\(\sqrt{81}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{81}\)?
#real-numbers
#rational-number
#perfect-square
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C अनावर्ती दशमलव / Non-recurring decimal
D ऋणात्मक संख्या / Negative number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
(81) एक पूर्ण वर्ग है। / (81) is a perfect square.
Step 2
Why this answer is correct
\(\sqrt{81}=9\), और (9) को \(\frac{9}{1}\) लिखा जा सकता है। / \(\sqrt{81}=9\), and (9) can be written as \(\frac{9}{1}\).
Step 3
Exam Tip
पूर्ण वर्ग का वर्गमूल हमेशा परिमेय होता है। / The square root of a perfect square is always rational.
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कौन-सा दशमलव अपरिमेय संख्या को दर्शाता है?
Which decimal represents an irrational number?
#real-numbers
#decimal-expansion
#irrational
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A \(0.272727\ldots\)
B (0.4)
C \(0.1234567891011\ldots\)
D (2.75)
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Correct Answer
C. \(0.1234567891011\ldots\)
Step 1
Concept
समाप्त या आवर्ती दशमलव परिमेय होते हैं। / Terminating or recurring decimals are rational.
Step 2
Why this answer is correct
\(0.1234567891011\ldots\) में कोई निश्चित दोहराव नहीं है, इसलिए यह अनवसानी और अनावर्ती है। / \(0.1234567891011\ldots\) has no fixed repeating pattern, so it is non-terminating and non-recurring.
Step 3
Exam Tip
अपरिमेय दशमलव पहचानने के लिए दोहराव का नियम जांचें। / To identify an irrational decimal, check for a repeating rule.
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\(\sqrt{28}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{28}\)?
#real-numbers
#radical-simplification
#sqrt28
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A \(2\sqrt{7}\)
B \(7\sqrt{2}\)
C \(4\sqrt{7}\)
D \(14\sqrt{2}\)
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Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
\(28=4 \times 7\) लिखें। / Write \(28=4 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{28}=\sqrt{4 \times 7}=2\sqrt{7}\)। / \(\sqrt{28}=\sqrt{4 \times 7}=2\sqrt{7}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय पूर्ण वर्ग गुणनखंड को बाहर निकालें। / While simplifying a square root, take the perfect square factor outside.
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\(\sqrt{2}\times\sqrt{18}\) का मान क्या होगा?
What is the value of \(\sqrt{2}\times\sqrt{18}\)?
#real-numbers
#radical-product
#rational-result
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A (6)
B \(\sqrt{20}\)
C \(2\sqrt{18}\)
D (36)
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Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा होती हैं। / When multiplying square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{18}=\sqrt{36}=6\)। / \(\sqrt{2}\times\sqrt{18}=\sqrt{36}=6\).
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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निम्नलिखित में से कौन-सा विकल्प परिमेय है?
Which of the following options is rational?
#real-numbers
#rational-number
#square-root
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A \(\sqrt{19}\)
B \(\sqrt{21}\)
C \(\sqrt{100}\)
D \(\sqrt{30}\)
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Correct Answer
C. \(\sqrt{100}\)
Step 1
Concept
परिमेय विकल्प खोजने के लिए पूर्ण वर्ग का वर्गमूल देखें। / To find the rational option, look for the square root of a perfect square.
Step 2
Why this answer is correct
(100) पूर्ण वर्ग है और \(\sqrt{100}=10\)। / (100) is a perfect square and \(\sqrt{100}=10\).
Step 3
Exam Tip
\(\sqrt{n}\) में यदि (n) पूर्ण वर्ग हो, तो उत्तर परिमेय होगा। / In \(\sqrt{n}\), if (n) is a perfect square, the value is rational.
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\(\sqrt{2}+5\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(\sqrt{2}+5\)?
#real-numbers
#irrational-sum
#sqrt2
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A यह परिमेय है / It is rational
B यह अपरिमेय है / It is irrational
C यह (7) है / It is (7)
D यह पूर्णांक है / It is an integer
Explanation opens after your attempt
Correct Answer
B. यह अपरिमेय है / It is irrational
Step 1
Concept
\(\sqrt{2}\) अपरिमेय है और (5) परिमेय है। / \(\sqrt{2}\) is irrational and (5) is rational.
Step 2
Why this answer is correct
परिमेय संख्या जोड़ने से अपरिमेय भाग समाप्त नहीं होता। / Adding a rational number does not remove the irrational part.
Step 3
Exam Tip
परिमेय और अपरिमेय का योग सामान्यतः अपरिमेय होता है। / The sum of a rational and an irrational number is generally irrational.
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\(\sqrt{48}\) को सरल करने पर क्या मिलेगा?
What do we get after simplifying \(\sqrt{48}\)?
#real-numbers
#simplify-radicals
#irrational
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A \(4\sqrt{3}\)
B \(3\sqrt{4}\)
C \(6\sqrt{2}\)
D \(8\sqrt{3}\)
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Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(48=16 \times 3\) है। / \(48=16 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{48}=\sqrt{16 \times 3}=4\sqrt{3}\)। / \(\sqrt{48}=\sqrt{16 \times 3}=4\sqrt{3}\).
Step 3
Exam Tip
सबसे बड़ा पूर्ण वर्ग लेने से सरल रूप सही और छोटा मिलता है। / Using the largest perfect square gives the simplest form.
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किस संख्या का दशमलव विस्तार समाप्त होता है?
Which number has a terminating decimal expansion?
#real-numbers
#terminating-decimal
#rational
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A \(\sqrt{5}\)
B \(\frac{3}{8}\)
C \(\sqrt{11}\)
D \(\sqrt{13}\)
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Correct Answer
B. \(\frac{3}{8}\)
Step 1
Concept
समाप्त दशमलव वाली संख्या परिमेय होती है। / A number with a terminating decimal is rational.
Step 2
Why this answer is correct
\(\frac{3}{8}=0.375\), इसलिए इसका दशमलव समाप्त होता है। / \(\frac{3}{8}=0.375\), so its decimal terminates.
Step 3
Exam Tip
भिन्न के हर में केवल (2) और (5) के गुणनखंड हों तो दशमलव समाप्त होता है। / If the denominator has only factors (2) and (5), the decimal terminates.
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\(\sqrt{7}+\sqrt{7}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{7}+\sqrt{7}\)?
#real-numbers
#radical-addition
#irrational
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A \(2\sqrt{7}\)
B \(\sqrt{14}\)
C \(7\sqrt{2}\)
D (14)
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Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
समान वर्गमूलों को समान पद की तरह जोड़ा जाता है। / Like radicals are added like like terms.
Step 2
Why this answer is correct
\(\sqrt{7}+\sqrt{7}=2\sqrt{7}\)। / \(\sqrt{7}+\sqrt{7}=2\sqrt{7}\).
Step 3
Exam Tip
जोड़ में अंदर की संख्याएँ जोड़कर \(\sqrt{14}\) नहीं लिखना चाहिए। / In addition, do not add the numbers inside roots to write \(\sqrt{14}\).
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\(\sqrt{7}-\sqrt{7}\) का मान क्या है?
What is the value of \(\sqrt{7}-\sqrt{7}\)?
#real-numbers
#irrational-difference
#zero
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A (0)
B \(\sqrt{14}\)
C (7)
D \(2\sqrt{7}\)
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Step 1
Concept
किसी संख्या में से वही संख्या घटाने पर शून्य मिलता है। / Subtracting a number from itself gives zero.
Step 2
Why this answer is correct
\(\sqrt{7}-\sqrt{7}=0\), और (0) परिमेय है। / \(\sqrt{7}-\sqrt{7}=0\), and (0) is rational.
Step 3
Exam Tip
अपरिमेय संख्याओं के साथ भी सामान्य घटाव नियम लागू होता है। / Normal subtraction rules also apply to irrational numbers.
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\(\sqrt{2}\) और \(\sqrt{5}\) के गुणनफल की प्रकृति क्या है?
What is the nature of the product of \(\sqrt{2}\) and \(\sqrt{5}\)?
#real-numbers
#irrational-product
#sqrt10
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{2}\times\sqrt{5}=\sqrt{10}\)। / \(\sqrt{2}\times\sqrt{5}=\sqrt{10}\).
Step 2
Why this answer is correct
(10) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{10}\) अपरिमेय है। / (10) is not a perfect square, so \(\sqrt{10}\) is irrational.
Step 3
Exam Tip
गुणन के बाद बने वर्गमूल की अंदर की संख्या जांचें। / After multiplication, check the number inside the new root.
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निम्नलिखित में से कौन-सा कथन सत्य है?
Which of the following statements is true?
#real-numbers
#true-statement
#irrational
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A हर अपरिमेय संख्या ऋणात्मक होती है / Every irrational number is negative
B हर परिमेय संख्या अपरिमेय होती है / Every rational number is irrational
C \(\sqrt{n}\) अपरिमेय हो सकता है जब (n) पूर्ण वर्ग न हो / \(\sqrt{n}\) can be irrational when (n) is not a perfect square
D हर दशमलव पूर्णांक होता है / Every decimal is an integer
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Correct Answer
C. \(\sqrt{n}\) अपरिमेय हो सकता है जब (n) पूर्ण वर्ग न हो / \(\sqrt{n}\) can be irrational when (n) is not a perfect square
Step 1
Concept
यदि (n) पूर्ण वर्ग नहीं है, तो \(\sqrt{n}\) परिमेय नहीं होता। / If (n) is not a perfect square, \(\sqrt{n}\) is not rational.
Step 2
Why this answer is correct
जैसे \(\sqrt{6}\) अपरिमेय है। / For example, \(\sqrt{6}\) is irrational.
Step 3
Exam Tip
सत्य कथन में उदाहरण लगाकर जांच करना आसान रहता है। / Testing a statement with an example makes it easier to judge.
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\(\sqrt{98}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{98}\)?
#real-numbers
#sqrt98
#simplification
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A \(7\sqrt{2}\)
B \(2\sqrt{7}\)
C \(14\sqrt{2}\)
D \(49\sqrt{2}\)
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Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
\(98=49 \times 2\) है। / \(98=49 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{98}=\sqrt{49 \times 2}=7\sqrt{2}\)। / \(\sqrt{98}=\sqrt{49 \times 2}=7\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग जैसे (49) को पहचानना सरलीकरण में मदद करता है। / Recognising larger perfect squares like (49) helps in simplification.
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\(\sqrt{3}\) और \(\sqrt{12}\) का योग क्या है?
What is the sum of \(\sqrt{3}\) and \(\sqrt{12}\)?
#real-numbers
#radical-addition
#sqrt3
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A \(3\sqrt{3}\)
B \(\sqrt{15}\)
C \(4\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) है। / \(\sqrt{12}=2\sqrt{3}\).
Step 2
Why this answer is correct
\(\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)। / \(\sqrt{3}+2\sqrt{3}=3\sqrt{3}\).
Step 3
Exam Tip
जोड़ से पहले वर्गमूलों को समान रूप में बदलें। / Before adding, convert radicals into like terms if possible.
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कौन-सी संख्या (4) और (5) के बीच स्थित अपरिमेय संख्या है?
Which number is an irrational number lying between (4) and (5)?
#real-numbers
#irrational-between-numbers
#sqrt17
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A \(\sqrt{17}\)
B \(\sqrt{16}\)
C \(\sqrt{25}\)
D (4.5)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{17}\)
Step 1
Concept
(16<17<25), इसलिए \(4<\sqrt{17}<5\)। / Since (16<17<25), \(4<\sqrt{17}<5\).
Step 2
Why this answer is correct
(17) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{17}\) अपरिमेय है। / (17) is not a perfect square, so \(\sqrt{17}\) is irrational.
Step 3
Exam Tip
अंतराल वाले प्रश्न में पास के पूर्ण वर्गों का उपयोग करें। / Use nearby perfect squares in interval questions.
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\(\frac{\sqrt{5}}{5}\) कैसी संख्या है?
What type of number is \(\frac{\sqrt{5}}{5}\)?
#real-numbers
#irrational-division
#sqrt5
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D प्राकृतिक / Natural
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{5}\) अपरिमेय है। / \(\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
अशून्य परिमेय संख्या (5) से भाग देने पर यह अपरिमेय ही रहती है। / Dividing it by the non-zero rational number (5) keeps it irrational.
Step 3
Exam Tip
हर में परिमेय संख्या होने से पूरा पद परिमेय नहीं हो जाता। / A rational denominator alone does not make the whole expression rational.
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निम्नलिखित में से कौन-सा युग्म एक परिमेय और एक अपरिमेय संख्या का है?
Which pair has one rational and one irrational number?
#real-numbers
#rational-irrational-pair
#mcq
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A \(3,\sqrt{6}\)
B \(\sqrt{2},\sqrt{3}\)
C \(5,\frac{7}{2}\)
D \(\sqrt{4},\sqrt{9}\)
Explanation opens after your attempt
Correct Answer
A. \(3,\sqrt{6}\)
Step 1
Concept
(3) परिमेय है। / (3) is rational.
Step 2
Why this answer is correct
\(\sqrt{6}\) अपरिमेय है क्योंकि (6) पूर्ण वर्ग नहीं है। / \(\sqrt{6}\) is irrational because (6) is not a perfect square.
Step 3
Exam Tip
युग्म में दोनों संख्याओं को अलग-अलग पहचानें। / In a pair, identify each number separately.
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\(\sqrt{125}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{125}\)?
#real-numbers
#square-root
#simplification
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A \(5\sqrt{5}\)
B \(25\sqrt{5}\)
C \(3\sqrt{5}\)
D \(5\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(125=25 \times 5\) लिखें। / Write \(125=25 \times 5\).
Step 2
Why this answer is correct
\(\sqrt{125}=\sqrt{25 \times 5}=5\sqrt{5}\)। / \(\sqrt{125}=\sqrt{25 \times 5}=5\sqrt{5}\).
Step 3
Exam Tip
पूर्ण वर्ग (25) को बाहर (5) के रूप में निकालें। / Take the perfect square (25) outside as (5).
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\(\sqrt{6}+\sqrt{6}+\sqrt{6}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{6}+\sqrt{6}+\sqrt{6}\)?
#real-numbers
#like-radicals
#addition
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A \(3\sqrt{6}\)
B \(\sqrt{18}\)
C \(6\sqrt{3}\)
D (18)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{6}\)
Step 1
Concept
तीन समान अपरिमेय पद जोड़े जा रहे हैं। / Three like irrational terms are being added.
Step 2
Why this answer is correct
\(\sqrt{6}+\sqrt{6}+\sqrt{6}=3\sqrt{6}\)। / \(\sqrt{6}+\sqrt{6}+\sqrt{6}=3\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूलों को गुणांक की तरह गिनें। / Count like radicals as coefficients.
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\(\sqrt{45}-\sqrt{20}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{45}-\sqrt{20}\)?
#real-numbers
#radical-subtraction
#sqrt5
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A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(\sqrt{25}\)
D \(3\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\).
Step 2
Why this answer is correct
\(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\)। / \(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को सरल करें। / Simplify both radicals before subtracting.
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\(\sqrt{2}\) का वर्ग किस प्रकार की संख्या है?
What type of number is the square of \(\sqrt{2}\)?
#real-numbers
#square-of-irrational
#rational-result
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A अपरिमेय / Irrational
B परिमेय / Rational
C अनवसानी अनावर्ती / Non-terminating non-recurring
D ऋणात्मक / Negative
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Step 1
Concept
(\(\sqrt{2}\)2 =2)। / (\(\sqrt{2}\)2 =2).
Step 2
Why this answer is correct
(2) परिमेय संख्या है क्योंकि इसे \(\frac{2}{1}\) लिखा जा सकता है। / (2) is rational because it can be written as \(\frac{2}{1}\).
Step 3
Exam Tip
अपरिमेय संख्या का वर्ग कभी-कभी परिमेय हो सकता है। / The square of an irrational number can sometimes be rational.
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यदि \(x=\sqrt{5}\), तो (5x) कैसी संख्या होगी?
If \(x=\sqrt{5}\), what type of number is (5x)?
#real-numbers
#irrational-product
#coefficient
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A परिमेय / Rational
B अपरिमेय / Irrational
C शून्य / Zero
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(x=\sqrt{5}\) अपरिमेय है। / \(x=\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
\(5x=5\sqrt{5}\), और (5) अशून्य परिमेय है। / \(5x=5\sqrt{5}\), and (5) is a non-zero rational number.
Step 3
Exam Tip
अपरिमेय संख्या को अशून्य परिमेय से गुणा करने पर परिणाम अपरिमेय रहता है। / Multiplying an irrational number by a non-zero rational number keeps it irrational.
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कौन-सा विकल्प अपरिमेय संख्या नहीं है?
Which option is not an irrational number?
#real-numbers
#not-irrational
#perfect-square
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A \(\sqrt{22}\)
B \(\sqrt{36}\)
C \(\sqrt{26}\)
D \(\sqrt{35}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{36}\)
Step 1
Concept
प्रश्न अपरिमेय नहीं पूछ रहा है, इसलिए परिमेय संख्या खोजें। / The question asks for the number that is not irrational, so find the rational one.
Step 2
Why this answer is correct
\(\sqrt{36}=6\), जो परिमेय है। / \(\sqrt{36}=6\), which is rational.
Step 3
Exam Tip
ऐसे प्रश्नों में नकारात्मक भाषा को ध्यान से पढ़ें। / Read negative wording carefully in MCQs.
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\(\sqrt{8}+\sqrt{18}\) का सरल रूप क्या होगा?
What is the simplified form of \(\sqrt{8}+\sqrt{18}\)?
#real-numbers
#radical-addition
#simplification
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A \(5\sqrt{2}\)
B \(2\sqrt{26}\)
C \(\sqrt{26}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\)। / \(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only after they become like radicals.
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निम्नलिखित में से कौन-सा कथन गलत है?
Which of the following statements is false?
#real-numbers
#false-statement
#perfect-square
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A \(0.121212\ldots\) परिमेय है / \(0.121212\ldots\) is rational
B \(\sqrt{23}\) अपरिमेय है / \(\sqrt{23}\) is irrational
C \(\sqrt{49}\) अपरिमेय है / \(\sqrt{49}\) is irrational
D \(\frac{5}{6}\) परिमेय है / \(\frac{5}{6}\) is rational
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{49}\) अपरिमेय है / \(\sqrt{49}\) is irrational
Step 1
Concept
\(\sqrt{49}=7\) होता है। / \(\sqrt{49}=7\).
Step 2
Why this answer is correct
(7) परिमेय है, इसलिए \(\sqrt{49}\) को अपरिमेय कहना गलत है। / (7) is rational, so saying \(\sqrt{49}\) is irrational is false.
Step 3
Exam Tip
गलत कथन चुनते समय पूर्ण वर्गों को जरूर जांचें। / While choosing a false statement, check perfect squares carefully.
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\(\sqrt{150}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{150}\)?
#real-numbers
#sqrt150
#radical-simplification
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A \(5\sqrt{6}\)
B \(6\sqrt{5}\)
C \(10\sqrt{15}\)
D \(15\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{6}\)
Step 1
Concept
\(150=25 \times 6\) लिखें। / Write \(150=25 \times 6\).
Step 2
Why this answer is correct
\(\sqrt{150}=\sqrt{25 \times 6}=5\sqrt{6}\)। / \(\sqrt{150}=\sqrt{25 \times 6}=5\sqrt{6}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड बाहर निकालकर बाकी गुणनखंड अंदर छोड़ें। / Take the perfect square factor outside and leave the remaining factor inside.
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\(\sqrt{5}\times\sqrt{20}\) का मान क्या होगा?
What is the value of \(\sqrt{5}\times\sqrt{20}\)?
#real-numbers
#radical-product
#rational-result
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A (10)
B \(\sqrt{25}\)
C \(5\sqrt{20}\)
D \(\sqrt{1000}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{5}\times\sqrt{20}=\sqrt{100}\)। / \(\sqrt{5}\times\sqrt{20}=\sqrt{100}\).
Step 2
Why this answer is correct
\(\sqrt{100}=10\), जो परिमेय संख्या है। / \(\sqrt{100}=10\), which is rational.
Step 3
Exam Tip
गुणन में पहले अंदर की संख्याओं का गुणन करें। / In multiplication, first multiply the numbers inside the roots.
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कौन-सी संख्या (5) और (6) के बीच स्थित है?
Which number lies between (5) and (6)?
#real-numbers
#comparison
#irrational-between
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A \(\sqrt{30}\)
B \(\sqrt{25}\)
C \(\sqrt{36}\)
D (6.5)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{30}\)
Step 1
Concept
(25<30<36), इसलिए \(5<\sqrt{30}<6\)। / Since (25<30<36), \(5<\sqrt{30}<6\).
Step 2
Why this answer is correct
(30) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{30}\) अपरिमेय है। / (30) is not a perfect square, so \(\sqrt{30}\) is irrational.
Step 3
Exam Tip
वर्गमूल की स्थिति जानने के लिए नजदीकी पूर्ण वर्ग देखें। / Use nearby perfect squares to locate a square root.
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\(\sqrt{200}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{200}\)?
#real-numbers
#sqrt200
#simplification
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A \(10\sqrt{2}\)
B \(20\sqrt{5}\)
C \(2\sqrt{100}\)
D \(100\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{2}\)
Step 1
Concept
\(200=100 \times 2\) है। / \(200=100 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{200}=\sqrt{100 \times 2}=10\sqrt{2}\)। / \(\sqrt{200}=\sqrt{100 \times 2}=10\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग (100) को पहचानने से उत्तर जल्दी मिलता है। / Recognising a large perfect square like (100) gives the answer quickly.
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\(\sqrt{3}+2\sqrt{3}\) किसके बराबर है?
What is \(\sqrt{3}+2\sqrt{3}\) equal to?
#real-numbers
#like-radicals
#addition
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A \(3\sqrt{3}\)
B \(2\sqrt{6}\)
C \(\sqrt{9}\)
D \(5\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
दोनों पदों में \(\sqrt{3}\) समान है। / Both terms have the same radical \(\sqrt{3}\).
Step 2
Why this answer is correct
\(1\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)। / \(1\sqrt{3}+2\sqrt{3}=3\sqrt{3}\).
Step 3
Exam Tip
समान वर्गमूलों में केवल गुणांक जोड़ें। / For like radicals, add only the coefficients.
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\(\sqrt{2}\) का लगभग मान किसके सबसे निकट है?
The approximate value of \(\sqrt{2}\) is closest to which number?
#real-numbers
#approximation
#sqrt2
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A (1.41)
B (1.90)
C (2.41)
D (0.41)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\) का मान लगभग (1.414) है। / The value of \(\sqrt{2}\) is about (1.414).
Step 2
Why this answer is correct
दिए गए विकल्पों में (1.41) सबसे निकट है। / Among the given options, (1.41) is closest.
Step 3
Exam Tip
सामान्य वर्गमूलों के लगभग मान याद रखने से तुलना आसान होती है। / Remembering approximate values of common roots helps in comparison.
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\(\sqrt{10}\) का मान किन दो पूर्णांकों के बीच होगा?
Between which two integers does \(\sqrt{10}\) lie?
#real-numbers
#comparison
#sqrt10
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A (1) और (2) / (1) and (2)
B (2) और (3) / (2) and (3)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
C. (3) और (4) / (3) and (4)
Step 1
Concept
(9<10<16) है।
Step 2
Why this answer is correct
इसलिए \(\sqrt{9}<\sqrt{10}<\sqrt{16}\), यानी \(3<\sqrt{10}<4\)। / So \(\sqrt{9}<\sqrt{10}<\sqrt{16}\), meaning \(3<\sqrt{10}<4\).
Step 3
Exam Tip
वर्गमूल की सीमा के लिए पास के पूर्ण वर्गों का उपयोग करें। / Use nearby perfect squares to find the range of a square root.
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\(\sqrt{63}\) को सरल कीजिए।
Simplify \(\sqrt{63}\).
#real-numbers
#sqrt63
#radical-simplification
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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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यदि \(y=\sqrt{11}\), तो \(y^2\) का मान क्या होगा?
If \(y=\sqrt{11}\), what is the value of \(y^2\)?
#real-numbers
#square-root
#square
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A (11)
B \(\sqrt{11}\)
C (121)
D (22)
Explanation opens after your attempt
Step 1
Concept
\(y=\sqrt{11}\) है। / \(y=\sqrt{11}\).
Step 2
Why this answer is correct
(y-2 =\(\sqrt{11}\)2 =11)। / (y-2 =\(\sqrt{11}\)2 =11).
Step 3
Exam Tip
वर्गमूल का वर्ग करने पर मूल संख्या मिलती है। / Squaring a square root gives the original number inside it.
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कौन-सा विकल्प दो अपरिमेय संख्याओं का ऐसा गुणनफल दिखाता है जो परिमेय है?
Which option shows a product of two irrational numbers that is rational?
#real-numbers
#irrational-product
#rational-result
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A \(\sqrt{3}\times\sqrt{3}\)
B \(\sqrt{2}\times\sqrt{5}\)
C \(\sqrt{7}\times\sqrt{11}\)
D \(\sqrt{5}\times\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\times\sqrt{3}\)
Step 1
Concept
\(\sqrt{3}\) अपरिमेय है। / \(\sqrt{3}\) is irrational.
Step 2
Why this answer is correct
\(\sqrt{3}\times\sqrt{3}=3\), जो परिमेय है। / \(\sqrt{3}\times\sqrt{3}=3\), which is rational.
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता। / The product of two irrational numbers is not always irrational.
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\(\sqrt{5}+0\) किसके बराबर है?
What is \(\sqrt{5}+0\) equal to?
#real-numbers
#zero-property
#irrational
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A \(\sqrt{5}\)
B (5)
C (0)
D \(\sqrt{0}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
शून्य जोड़ने से संख्या नहीं बदलती। / Adding zero does not change a number.
Step 2
Why this answer is correct
\(\sqrt{5}+0=\sqrt{5}\), जो अपरिमेय है। / \(\sqrt{5}+0=\sqrt{5}\), which is irrational.
Step 3
Exam Tip
शून्य के साथ भी संख्या की मूल प्रकृति समझें। / Even with zero, understand the original nature of the number.
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\(\sqrt{6}\) का दशमलव विस्तार कैसा होगा?
What kind of decimal expansion does \(\sqrt{6}\) have?
#real-numbers
#decimal-expansion
#sqrt6
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A समाप्त / Terminating
B आवर्ती / Recurring
C अनवसानी और अनावर्ती / Non-terminating and non-recurring
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
C. अनवसानी और अनावर्ती / Non-terminating and non-recurring
Step 1
Concept
(6) पूर्ण वर्ग नहीं है। / (6) is not a perfect square.
Step 2
Why this answer is correct
इसलिए \(\sqrt{6}\) अपरिमेय है और इसका दशमलव अनवसानी अनावर्ती होगा। / So \(\sqrt{6}\) is irrational and its decimal is non-terminating and non-recurring.
Step 3
Exam Tip
अपरिमेय संख्या में स्थिर दोहराव नहीं होता। / An irrational number has no fixed repeating pattern.
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\(\sqrt{90}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{90}\)?
#real-numbers
#sqrt90
#simplification
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A \(3\sqrt{10}\)
B \(9\sqrt{10}\)
C \(10\sqrt{9}\)
D \(5\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{10}\)
Step 1
Concept
\(90=9 \times 10\) लिखें। / Write \(90=9 \times 10\).
Step 2
Why this answer is correct
\(\sqrt{90}=\sqrt{9 \times 10}=3\sqrt{10}\)। / \(\sqrt{90}=\sqrt{9 \times 10}=3\sqrt{10}\).
Step 3
Exam Tip
पूर्ण वर्ग को बाहर निकालकर शेष भाग अंदर रखें। / Take the perfect square outside and keep the remaining part inside.
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कौन-सी संख्या \(\sqrt{12}\) के बराबर है?
Which number is equal to \(\sqrt{12}\)?
#real-numbers
#equivalent-radicals
#sqrt12
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A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(4\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(12=4 \times 3\) है। / \(12=4 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{12}=2\sqrt{3}\)। / \(\sqrt{12}=2\sqrt{3}\).
Step 3
Exam Tip
बराबर रूप पहचानने के लिए वर्गमूल को सरल करना जरूरी है। / To identify an equivalent form, simplify the square root first.
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\(\sqrt{5}\) और \(-\sqrt{5}\) का योग क्या है?
What is the sum of \(\sqrt{5}\) and \(-\sqrt{5}\)?
#real-numbers
#opposites
#irrational
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A (0)
B (5)
C (-5)
D \(2\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
दोनों पद एक-दूसरे के विपरीत हैं। / The two terms are opposites of each other.
Step 2
Why this answer is correct
(\sqrt{5}+\(-\sqrt{5}\)=0)। / (\sqrt{5}+\(-\sqrt{5}\)=0).
Step 3
Exam Tip
विपरीत पदों का योग हमेशा शून्य होता है। / The sum of opposite terms is always zero.
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यदि (a) अपरिमेय है और (r) अशून्य परिमेय है, तो (ra) किस प्रकार की संख्या होगी?
If (a) is irrational and (r) is a non-zero rational number, what type of number is (ra)?
#real-numbers
#irrational-rule
#nonzero-rational
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A परिमेय / Rational
B अपरिमेय / Irrational
C हमेशा शून्य / Always zero
D हमेशा प्राकृतिक / Always natural
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
अशून्य परिमेय गुणक अपरिमेयता को समाप्त नहीं करता। / A non-zero rational multiplier does not remove irrationality.
Step 2
Why this answer is correct
जैसे \(3\sqrt{2}\) अपरिमेय है। / For example, \(3\sqrt{2}\) is irrational.
Step 3
Exam Tip
यहां अशून्य शर्त जरूरी है क्योंकि शून्य से गुणा करने पर परिणाम शून्य होगा। / The non-zero condition is important because multiplying by zero gives zero.
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\(\sqrt{112}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{112}\)?
#real-numbers
#sqrt112
#radical-simplification
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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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निम्नलिखित में कौन-सा अपरिमेय संख्या का दशमलव रूप हो सकता है?
Which of the following can be the decimal form of an irrational number?
#real-numbers
#decimal-form
#irrational
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A \(0.6666\ldots\)
B (0.2500)
C \(1.41421356\ldots\) बिना निश्चित दोहराव / \(1.41421356\ldots\) with no fixed repetition
D (3.000)
Explanation opens after your attempt
Correct Answer
C. \(1.41421356\ldots\) बिना निश्चित दोहराव / \(1.41421356\ldots\) with no fixed repetition
Step 1
Concept
आवर्ती या समाप्त दशमलव परिमेय होते हैं। / Recurring or terminating decimals are rational.
Step 2
Why this answer is correct
बिना निश्चित दोहराव वाला अनवसानी दशमलव अपरिमेय हो सकता है। / A non-terminating decimal without fixed repetition can be irrational.
Step 3
Exam Tip
केवल लंबा दशमलव देखकर नहीं, दोहराव देखकर निर्णय लें। / Do not judge only by length; check for repetition.
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\(\sqrt{147}\) को सरल कीजिए।
Simplify \(\sqrt{147}\).
#real-numbers
#sqrt147
#simplification
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A \(7\sqrt{3}\)
B \(3\sqrt{7}\)
C \(21\sqrt{3}\)
D \(49\sqrt{3}\)
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Correct Answer
A. \(7\sqrt{3}\)
Step 1
Concept
\(147=49 \times 3\) लिखें। / Write \(147=49 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{147}=\sqrt{49 \times 3}=7\sqrt{3}\)। / \(\sqrt{147}=\sqrt{49 \times 3}=7\sqrt{3}\).
Step 3
Exam Tip
पूर्ण वर्ग (49) को पहचानना यहां मुख्य कदम है। / Recognising the perfect square (49) is the main step here.
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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
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A (8)
B \(\sqrt{34}\)
C (16)
D \(4\sqrt{2}\)
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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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\(\sqrt{3}\) का लगभग मान कौन-सा है?
What is the approximate value of \(\sqrt{3}\)?
#real-numbers
#approximation
#sqrt3
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A (1.73)
B (1.31)
C (2.73)
D (3.14)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\) का मान लगभग (1.732) है। / \(\sqrt{3}\) is approximately (1.732).
Step 2
Why this answer is correct
इसलिए (1.73) सबसे सही निकट मान है। / So (1.73) is the closest correct value.
Step 3
Exam Tip
अनुमान के लिए सामान्य वर्गमूलों के मान याद रखें। / For estimation, remember common square-root values.
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कौन-सा विकल्प \(\sqrt{24}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{24}\)?
#real-numbers
#sqrt24
#simplification
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A \(2\sqrt{6}\)
B \(4\sqrt{6}\)
C \(6\sqrt{2}\)
D \(12\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{6}\)
Step 1
Concept
\(24=4 \times 6\) है। / \(24=4 \times 6\).
Step 2
Why this answer is correct
\(\sqrt{24}=\sqrt{4 \times 6}=2\sqrt{6}\)। / \(\sqrt{24}=\sqrt{4 \times 6}=2\sqrt{6}\).
Step 3
Exam Tip
यदि अंदर (6) बचे तो वह आगे सरल नहीं होगा क्योंकि (6) में पूर्ण वर्ग गुणनखंड नहीं है। / If (6) remains inside, it cannot be simplified further because it has no perfect square factor.
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\(\sqrt{13}\) का मान किन दो पूर्णांकों के बीच है?
Between which two integers does \(\sqrt{13}\) lie?
#real-numbers
#comparison
#sqrt13
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A (2) और (3) / (2) and (3)
B (3) और (4) / (3) and (4)
C (4) और (5) / (4) and (5)
D (5) और (6) / (5) and (6)
Explanation opens after your attempt
Correct Answer
B. (3) और (4) / (3) and (4)
Step 1
Concept
(9<13<16) है।
Step 2
Why this answer is correct
इसलिए \(3<\sqrt{13}<4\)। / Therefore, \(3<\sqrt{13}<4\).
Step 3
Exam Tip
वर्गमूल की तुलना के लिए पास के पूर्ण वर्ग बहुत उपयोगी होते हैं। / Nearby perfect squares are very useful for comparing square roots.
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निम्नलिखित में से कौन-सा परिणाम अपरिमेय है?
Which of the following results is irrational?
#real-numbers
#irrational-result
#radicals
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A \(\sqrt{2}+\sqrt{8}\)
B \(\sqrt{4}+\sqrt{9}\)
C \(\sqrt{5}\times\sqrt{5}\)
D \(\sqrt{16}-\sqrt{9}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}+\sqrt{8}\)
Step 1
Concept
\(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\)। / \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(3\sqrt{2}\) अपरिमेय है। / \(3\sqrt{2}\) is irrational.
Step 3
Exam Tip
विकल्पों में परिणाम निकालकर ही संख्या की प्रकृति तय करें। / In options, simplify the result before deciding its nature.
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