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advanced-surd MCQ Questions for Class 10

advanced-surd se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

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4 questions tagged with advanced-surd.

Question 1/4 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

\(\frac{\sqrt{17}+\sqrt{13}}{\sqrt{17}-\sqrt{13}}\) का सरलतम परिमेयकृत रूप क्या है?

What is the simplest rationalized form of \(\frac{\sqrt{17}+\sqrt{13}}{\sqrt{17}-\sqrt{13}}\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{15+\sqrt{221}}{2}\)

Step 1

Concept

Multiplying by the conjugate gives \(\frac{30+2\sqrt{221}}{4}=\frac{15+\sqrt{221}}{2}\). In exams divide by the common factor at the end.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{15+\sqrt{221}}{2}\). Multiplying by the conjugate gives \(\frac{30+2\sqrt{221}}{4}=\frac{15+\sqrt{221}}{2}\). In exams divide by the common factor at the end.

Step 3

Exam Tip

हर के संयुग्मी से गुणा करने पर \(\frac{30+2\sqrt{221}}{4}=\frac{15+\sqrt{221}}{2}\) मिलता है। परीक्षा में अंत में समान गुणनखंड से भाग जरूर करें।

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Question 2/4 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\) का परिमेयकृत रूप क्या है?

What is the rationalized form of \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{4-\sqrt{15}}{2}\)

Step 1

Concept

Multiplying by the conjugate gives numerator (\(\sqrt{5}-\sqrt{3}\)2=8-2\sqrt{15}) and denominator (2). So the value is \(4-\sqrt{15}\) and the correct simple option is A.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{4-\sqrt{15}}{2}\). Multiplying by the conjugate gives numerator (\(\sqrt{5}-\sqrt{3}\)2=8-2\sqrt{15}) and denominator (2). So the value is \(4-\sqrt{15}\) and the correct simple option is A.

Step 3

Exam Tip

हर के संयुग्मी से गुणा करने पर अंश (\(\sqrt{5}-\sqrt{3}\)2=8-2\sqrt{15}) और हर (2) बनता है। इसलिए मान \(4-\sqrt{15}\) है पर सही सरल विकल्प A है।

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Question 3/4 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

\(\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\) का परिमेयकृत रूप क्या है?

What is the rationalized form of \(\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\)?

Explanation opens after your attempt
Correct Answer

A. \(5+2\sqrt{6}\)

Step 1

Concept

Multiplying by the conjugate of the denominator gives denominator (1) and numerator (\(\sqrt{3}+\sqrt{2}\)2=5+2\sqrt{6}). In exams apply the conjugate in one step.

Step 2

Why this answer is correct

The correct answer is A. \(5+2\sqrt{6}\). Multiplying by the conjugate of the denominator gives denominator (1) and numerator (\(\sqrt{3}+\sqrt{2}\)2=5+2\sqrt{6}). In exams apply the conjugate in one step.

Step 3

Exam Tip

हर के संयुग्मी से गुणा करने पर हर (1) और अंश (\(\sqrt{3}+\sqrt{2}\)2=5+2\sqrt{6}) बनता है। परीक्षा में एक ही चरण में संयुग्मी लगाएं।

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Question 4/4 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि \(x=3+\sqrt{10}\), तो \(x+\frac{1}{x}\) का मान क्या है?

If \(x=3+\sqrt{10}\), what is the value of \(x+\frac{1}{x}\)?

Explanation opens after your attempt
Correct Answer

A. \(2\sqrt{10}\)

Step 1

Concept

\(\frac{1}{3+\sqrt{10}}=\sqrt{10}-3\), so the sum is \(2\sqrt{10}\). In exams rationalize the reciprocal first.

Step 2

Why this answer is correct

The correct answer is A. \(2\sqrt{10}\). \(\frac{1}{3+\sqrt{10}}=\sqrt{10}-3\), so the sum is \(2\sqrt{10}\). In exams rationalize the reciprocal first.

Step 3

Exam Tip

\(\frac{1}{3+\sqrt{10}}=\sqrt{10}-3\), इसलिए योग \(2\sqrt{10}\) है। परीक्षा में पहले व्युत्क्रम को परिमेयकृत करें।

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