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nested-root MCQ Questions for Class 10

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

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2 questions tagged with nested-root.

Question 1/2 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{10+\sqrt{96}}\) का सरल रूप है?

Which option is the simplified form of \(\sqrt{10+\sqrt{96}}\)?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{6}+\sqrt{4}\)

Step 1

Concept

(\(\sqrt{6}+2\)2=6+4+4\sqrt{6}=10+\sqrt{96}). Hence \(\sqrt{6}+\sqrt{4}\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{6}+\sqrt{4}\). (\(\sqrt{6}+2\)2=6+4+4\sqrt{6}=10+\sqrt{96}). Hence \(\sqrt{6}+\sqrt{4}\) is correct.

Step 3

Exam Tip

(\(\sqrt{6}+2\)2=6+4+4\sqrt{6}=10+\sqrt{96}) है। इसलिए \(\sqrt{6}+\sqrt{4}\) सही रूप है।

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Question 2/2 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

कौन सा विकल्प \(\sqrt{3+\sqrt{5}}\) की प्रकृति निश्चित रूप से बताता है?

Which option definitely describes the nature of \(\sqrt{3+\sqrt{5}}\)?

Explanation opens after your attempt
Correct Answer

A. अपरिमेय वास्तविक संख्याIrrational real number

Step 1

Concept

If it were rational, its square \(3+\sqrt{5}\) would be rational, which it is not. Hence it is real irrational.

Step 2

Why this answer is correct

The correct answer is A. अपरिमेय वास्तविक संख्या / Irrational real number. If it were rational, its square \(3+\sqrt{5}\) would be rational, which it is not. Hence it is real irrational.

Step 3

Exam Tip

यदि यह परिमेय होता तो उसका वर्ग \(3+\sqrt{5}\) परिमेय होता, जो नहीं है। इसलिए यह वास्तविक अपरिमेय है।

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