19 results found for "rational-expression" in Class 10.
Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि (p) और (q) परिमेय संख्याएं हैं तथा \(p+q\sqrt{5}\) परिमेय है, तो (q) के बारे में क्या सही है?
If (p) and (q) are rational numbers and \(p+q\sqrt{5}\) is rational, what is true about (q)?
#rational-expression
#irrational-coefficient
#reasoning
A (q=0)
B (q=1)
C \(q=\sqrt{5}\)
D (q=p)
Explanation opens after your attempt
Step 1
Concept
If \(q\ne0\), then \(q\sqrt{5}\) is irrational and the sum cannot be rational. In exams check the possibility of a zero coefficient.
Step 2
Why this answer is correct
The correct answer is A. (q=0). If \(q\ne0\), then \(q\sqrt{5}\) is irrational and the sum cannot be rational. In exams check the possibility of a zero coefficient.
Step 3
Exam Tip
यदि \(q\ne0\), तो \(q\sqrt{5}\) अपरिमेय होगा और योग परिमेय नहीं हो सकता। परीक्षा में शून्य गुणांक की संभावना देखें।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि (x) अपरिमेय है, तो (\(x+\sqrt{2}\)-\(x-\sqrt{2}\)) किसके बराबर है?
If (x) is irrational, what is (\(x+\sqrt{2}\)-\(x-\sqrt{2}\)) equal to?
#algebra
#irrational-expression
#simplification
A \(2\sqrt{2}\)
B (2x)
C (0)
D \(\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{2}\)
Step 1
Concept
The like (x) terms cancel and the value left is \(2\sqrt{2}\). In exams do not be confused by the type of number during algebraic simplification.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{2}\). The like (x) terms cancel and the value left is \(2\sqrt{2}\). In exams do not be confused by the type of number during algebraic simplification.
Step 3
Exam Tip
समान (x) पद कट जाते हैं और मान \(2\sqrt{2}\) बचता है। परीक्षा में बीजीय सरलीकरण में संख्या के प्रकार से भ्रमित न हों।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि \(x=\sqrt{2}+\sqrt{5}\), तो (x) किस द्विघात समीकरण को संतुष्ट करता है?
If \(x=\sqrt{2}+\sqrt{5}\), which quadratic equation is satisfied by (x)?
#irrational-expression
#polynomial-equation
#advanced
A \(x^2-14x+9=0\)
B \(x^4-14x^2+9=0\)
C \(x^2-7=0\)
D \(x^4+14x^2+9=0\)
Explanation opens after your attempt
Correct Answer
B. \(x^4-14x^2+9=0\)
Step 1
Concept
From \(x^2=7+2\sqrt{10}\), we get (\(x^2-7\)2 =40). Hence \(x^4-14x^2+9=0\).
Step 2
Why this answer is correct
The correct answer is B. \(x^4-14x^2+9=0\). From \(x^2=7+2\sqrt{10}\), we get (\(x^2-7\)2 =40). Hence \(x^4-14x^2+9=0\).
Step 3
Exam Tip
\(x^2=7+2\sqrt{10}\) से (\(x^2-7\)2 =40) मिलता है। इसलिए \(x^4-14x^2+9=0\) है।
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Question
Hard Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प \(8-\sqrt{m}\) को अपरिमेय बनाता है?
Which option makes \(8-\sqrt{m}\) irrational?
#perfect-square
#irrational-expression
#reasoning
A (m=180)
B (m=169)
C (m=144)
D (m=121)
Explanation opens after your attempt
Correct Answer
A. (m=180)
Step 1
Concept
(180) is not a perfect square so \(\sqrt{180}\) is irrational. Subtracting an irrational from a rational gives an irrational result.
Step 2
Why this answer is correct
The correct answer is A. (m=180). (180) is not a perfect square so \(\sqrt{180}\) is irrational. Subtracting an irrational from a rational gives an irrational result.
Step 3
Exam Tip
(180) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{180}\) अपरिमेय है। परिमेय से अपरिमेय घटाने पर परिणाम अपरिमेय होता है।
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Question
Medium Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 27
कौन सा विकल्प \(12-\sqrt{m}\) को परिमेय बनाता है?
Which option makes \(12-\sqrt{m}\) rational?
#perfect-square
#rational-expression
#reasoning
A (m=225)
B (m=226)
C (m=227)
D (m=228)
Explanation opens after your attempt
Correct Answer
A. (m=225)
Step 1
Concept
\(\sqrt{225}=15\) is rational so \(12-\sqrt{225}\) will be rational. The root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. (m=225). \(\sqrt{225}=15\) is rational so \(12-\sqrt{225}\) will be rational. The root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{225}=15\) परिमेय है इसलिए \(12-\sqrt{225}\) परिमेय होगा। पूर्ण वर्ग की जड़ परिमेय होती है।
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Question
Medium Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 27
कौन सा विकल्प \(4+\sqrt{m}\) को अपरिमेय बनाता है?
Which option makes \(4+\sqrt{m}\) irrational?
#perfect-square
#irrational-expression
#reasoning
A (m=98)
B (m=100)
C (m=121)
D (m=144)
Explanation opens after your attempt
Step 1
Concept
(98) is not a perfect square so \(\sqrt{98}\) is irrational. Adding rational (4) still gives an irrational result.
Step 2
Why this answer is correct
The correct answer is A. (m=98). (98) is not a perfect square so \(\sqrt{98}\) is irrational. Adding rational (4) still gives an irrational result.
Step 3
Exam Tip
(98) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{98}\) अपरिमेय है। परिमेय संख्या (4) जोड़ने पर भी परिणाम अपरिमेय रहता है।
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Question
Medium Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
कौन सा विकल्प \(5+\sqrt{m}\) को परिमेय बनाता है?
Which option makes \(5+\sqrt{m}\) rational?
#perfect-square
#rational-expression
#reasoning
A (m=121)
B (m=122)
C (m=123)
D (m=124)
Explanation opens after your attempt
Correct Answer
A. (m=121)
Step 1
Concept
\(\sqrt{121}=11\) is rational so \(5+\sqrt{121}\) will be rational. The root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. (m=121). \(\sqrt{121}=11\) is rational so \(5+\sqrt{121}\) will be rational. The root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{121}=11\) परिमेय है इसलिए \(5+\sqrt{121}\) परिमेय होगा। पूर्ण वर्ग वाली जड़ परिमेय होती है।
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Question
Medium Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
कौन सा विकल्प \(9-\sqrt{m}\) को परिमेय बनाता है?
Which option makes \(9-\sqrt{m}\) rational?
#perfect-square
#rational-expression
#reasoning
A (m=100)
B (m=101)
C (m=102)
D (m=103)
Explanation opens after your attempt
Correct Answer
A. (m=100)
Step 1
Concept
\(\sqrt{100}=10\) is rational so \(9-\sqrt{100}\) will be rational. The root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. (m=100). \(\sqrt{100}=10\) is rational so \(9-\sqrt{100}\) will be rational. The root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{100}=10\) परिमेय है इसलिए \(9-\sqrt{100}\) परिमेय होगा। पूर्ण वर्ग वाली जड़ परिमेय होती है।
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Question
Medium Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 26
कौन सा विकल्प \(2+\sqrt{m}\) को अपरिमेय बनाता है?
Which option makes \(2+\sqrt{m}\) irrational?
#perfect-square
#irrational-expression
#reasoning
A (m=45)
B (m=49)
C (m=64)
D (m=81)
Explanation opens after your attempt
Step 1
Concept
(45) is not a perfect square so \(\sqrt{45}\) is irrational. Adding rational (2) keeps it irrational.
Step 2
Why this answer is correct
The correct answer is A. (m=45). (45) is not a perfect square so \(\sqrt{45}\) is irrational. Adding rational (2) keeps it irrational.
Step 3
Exam Tip
(45) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{45}\) अपरिमेय है। परिमेय (2) जोड़ने पर परिणाम अपरिमेय रहता है।
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Question
Medium Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि \(2+\sqrt{m}\) अपरिमेय है और (m) धनात्मक पूर्णांक है तो कौन सा (m) हो सकता है?
If \(2+\sqrt{m}\) is irrational and (m) is a positive integer, which (m) can be correct?
#perfect-square
#irrational-expression
#reasoning
A (18)
B (16)
C (25)
D (36)
Explanation opens after your attempt
Step 1
Concept
(18) is not a perfect square so \(\sqrt{18}\) is irrational. The roots of the other options are rational.
Step 2
Why this answer is correct
The correct answer is A. (18). (18) is not a perfect square so \(\sqrt{18}\) is irrational. The roots of the other options are rational.
Step 3
Exam Tip
(18) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{18}\) अपरिमेय है। बाकी विकल्पों की जड़ परिमेय है।
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Question
Medium Mathematics
Real Numbers 5: Irrational numbers Class 10 Level 15
\(\sqrt{7}+\sqrt{28}+\sqrt{63}\) की प्रकृति क्या है?
What is the nature of \(\sqrt{7}+\sqrt{28}+\sqrt{63}\)?
#real-numbers
#irrational-expression
#radicals
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
\(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{63}=3\sqrt{7}\).
Step 2
Why this answer is correct
The total is \(6\sqrt{7}\), which is irrational.
Step 3
Exam Tip
Simplify an expression before deciding its nature. चरण 1: \(\sqrt{28}=2\sqrt{7}\) और \(\sqrt{63}=3\sqrt{7}\)। चरण 2: कुल योग \(6\sqrt{7}\) है, जो अपरिमेय है। चरण 3: किसी अभिव्यक्ति की प्रकृति तय करने से पहले उसे सरल करें।
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Question
Medium Mathematics
Real Numbers 5: Irrational numbers Class 10 Level 15
(\left\(\sqrt{11}+2\right\)2 ) का मान क्या है?
What is the value of (\left\(\sqrt{11}+2\right\)2 )?
#real-numbers
#irrational-expression
#algebra
A \(15+4\sqrt{11}\)
B \(13+2\sqrt{11}\)
C \(15+2\sqrt{11}\)
D \(11+4\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. \(15+4\sqrt{11}\)
Step 1
Concept
Use ((a+b)2 =a-2 +2ab+b-2 ).
Step 2
Why this answer is correct
(\(\sqrt{11}\)2 +2\sqrt{11}\times2+22 =11+4\sqrt{11}+4=15+4\sqrt{11}).
Step 3
Exam Tip
Forgetting the middle term (2ab) is a common mistake. चरण 1: ((a+b)2 =a-2 +2ab+b-2 ) लगाएं। चरण 2: (\(\sqrt{11}\)2 +2\sqrt{11}\times2+22 =11+4\sqrt{11}+4=15+4\sqrt{11})। चरण 3: मध्य पद (2ab) को भूलना सामान्य गलती है।
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Question
Medium Mathematics
Real Numbers 5: Irrational numbers Class 10 Level 15
यदि \(x=7+\sqrt{13}\), तो (x-7) कैसी संख्या है?
If \(x=7+\sqrt{13}\), what type of number is (x-7)?
#real-numbers
#irrational-expression
#sqrt13
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
(x-7=\(7+\sqrt{13}\)-7).
Step 2
Why this answer is correct
This leaves \(\sqrt{13}\), which is irrational.
Step 3
Exam Tip
In such expressions, first subtract the matching rational part. चरण 1: (x-7=\(7+\sqrt{13}\)-7) होगा। चरण 2: इससे \(\sqrt{13}\) बचता है, जो अपरिमेय है। चरण 3: ऐसी अभिव्यक्तियों में पहले समान परिमेय भाग घटाएं।
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Question
Medium Mathematics
Real Numbers 5: Irrational numbers Class 10 Level 14
\(\sqrt{5}+\sqrt{20}+\sqrt{45}\) की प्रकृति क्या है?
What is the nature of \(\sqrt{5}+\sqrt{20}+\sqrt{45}\)?
#real-numbers
#irrational-expression
#radicals
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
\(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
The total is \(6\sqrt{5}\), which is irrational.
Step 3
Exam Tip
Simplify an expression before deciding its nature. चरण 1: \(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\)। चरण 2: कुल योग \(6\sqrt{5}\) है, जो अपरिमेय है। चरण 3: किसी अभिव्यक्ति की प्रकृति तय करने से पहले उसे सरल करें।
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Question
Medium Mathematics
Real Numbers 5: Irrational numbers Class 10 Level 14
(\left\(\sqrt{7}+1\right\)2 ) का मान क्या है?
What is the value of (\left\(\sqrt{7}+1\right\)2 )?
#real-numbers
#irrational-expression
#algebra
A \(8+2\sqrt{7}\)
B \(7+\sqrt{7}\)
C \(8+\sqrt{7}\)
D \(9+2\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(8+2\sqrt{7}\)
Step 1
Concept
Use ((a+b)2 =a-2 +2ab+b-2 ).
Step 2
Why this answer is correct
(\(\sqrt{7}\)2 +2\sqrt{7}\times1+12 =7+2\sqrt{7}+1=8+2\sqrt{7}).
Step 3
Exam Tip
Forgetting the middle term (2ab) is a common mistake. चरण 1: ((a+b)2 =a-2 +2ab+b-2 ) लगाएं। चरण 2: (\(\sqrt{7}\)2 +2\sqrt{7}\times1+12 =7+2\sqrt{7}+1=8+2\sqrt{7})। चरण 3: मध्य पद (2ab) को भूलना सामान्य गलती है।
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Question
Medium Mathematics
Real Numbers 5: Irrational numbers Class 10 Level 14
यदि \(x=4+\sqrt{7}\), तो (x-4) कैसी संख्या है?
If \(x=4+\sqrt{7}\), what type of number is (x-4)?
#real-numbers
#irrational-expression
#sqrt7
A परिमेय / Rational
B पूर्णांक / Integer
C अपरिमेय / Irrational
D प्राकृतिक / Natural
Explanation opens after your attempt
Correct Answer
C. अपरिमेय / Irrational
Step 1
Concept
(x-4=\(4+\sqrt{7}\)-4).
Step 2
Why this answer is correct
This leaves \(\sqrt{7}\), which is irrational.
Step 3
Exam Tip
First simplify the expression, then identify the nature of the number. चरण 1: (x-4=\(4+\sqrt{7}\)-4) होगा। चरण 2: इससे \(\sqrt{7}\) बचता है, जो अपरिमेय है। चरण 3: पहले अभिव्यक्ति को सरल करें, फिर संख्या की प्रकृति बताएं।
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Question
Medium Mathematics
Real Numbers 5: Irrational numbers Class 10 Level 13
\(\sqrt{3}+\sqrt{12}+\sqrt{27}\) की प्रकृति क्या है?
What is the nature of \(\sqrt{3}+\sqrt{12}+\sqrt{27}\)?
#real-numbers
#irrational-expression
#radicals
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
\(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
The total is \(6\sqrt{3}\), which is irrational.
Step 3
Exam Tip
Decide the nature of the number only after simplification. चरण 1: \(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\)। चरण 2: कुल योग \(6\sqrt{3}\) है, जो अपरिमेय है। चरण 3: सरलीकरण के बाद ही संख्या की प्रकृति तय करें।
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Question
Medium Mathematics
Real Numbers 5: Irrational numbers Class 10 Level 13
(\left\(\sqrt{5}+2\right\)2 ) का मान क्या है?
What is the value of (\left\(\sqrt{5}+2\right\)2 )?
#real-numbers
#irrational-expression
#algebra
A \(9+4\sqrt{5}\)
B \(7+2\sqrt{5}\)
C \(5+4\sqrt{5}\)
D \(9+\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(9+4\sqrt{5}\)
Step 1
Concept
Use ((a+b)2 =a-2 +2ab+b-2 ).
Step 2
Why this answer is correct
(\(\sqrt{5}\)2 +2\(\sqrt{5}\)(2)+22 =5+4\sqrt{5}+4=9+4\sqrt{5}).
Step 3
Exam Tip
Missing the middle term (2ab) is a common mistake. चरण 1: ((a+b)2 =a-2 +2ab+b-2 ) लगाएं। चरण 2: (\(\sqrt{5}\)2 +2\(\sqrt{5}\)(2)+22 =5+4\sqrt{5}+4=9+4\sqrt{5})। चरण 3: मध्य पद (2ab) को छोड़ना सामान्य गलती है।
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Question
Medium Mathematics
Real Numbers 5: Irrational numbers Class 10 Level 13
यदि \(x=3+\sqrt{5}\), तो (x-3) किस प्रकार की संख्या है?
If \(x=3+\sqrt{5}\), what type of number is (x-3)?
#real-numbers
#irrational-expression
#sqrt5
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
(x-3=\(3+\sqrt{5}\)-3).
Step 2
Why this answer is correct
This leaves \(\sqrt{5}\), which is irrational.
Step 3
Exam Tip
Simplify the expression before deciding the nature of the number. चरण 1: (x-3=\(3+\sqrt{5}\)-3) होगा। चरण 2: इससे \(\sqrt{5}\) बचता है, जो अपरिमेय है। चरण 3: अभिव्यक्ति को सरल करके संख्या की प्रकृति तय करें।
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