Hard Mathematics Polynomials 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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Mathematics Answer, Explanation and Revision Hints

कौन सा विकल्प \(\sqrt{3+\sqrt{5}}\) की प्रकृति निश्चित रूप से बताता है? / Which option definitely describes the nature of \(\sqrt{3+\sqrt{5}}\)?

Correct Answer: A. अपरिमेय वास्तविक संख्या / Irrational real number. Explanation: यदि यह परिमेय होता तो उसका वर्ग \(3+\sqrt{5}\) परिमेय होता, जो नहीं है। इसलिए यह वास्तविक अपरिमेय है। / If it were rational, its square \(3+\sqrt{5}\) would be rational, which it is not. Hence it is real irrational.

Which concept should I revise for this Mathematics MCQ?

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

What exam hint can help solve this Mathematics question?

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

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