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irrational square root MCQ Questions for Class 10

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3 questions tagged with irrational square root.

Question 1/3 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि \(\sqrt{m}\) अपरिमेय है और (m) धनात्मक पूर्णांक है, तो (m) के बारे में सही निष्कर्ष कौन सा है?

If \(\sqrt{m}\) is irrational and (m) is a positive integer, which conclusion about (m) is correct?

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Correct Answer

A. (m) पूर्ण वर्ग नहीं है(m) is not a perfect square

Step 1

Concept

The square root of a perfect square is an integer, so for an irrational square root (m) is not a perfect square. In exams identifying perfect squares is important.

Step 2

Why this answer is correct

The correct answer is A. (m) पूर्ण वर्ग नहीं है / (m) is not a perfect square. The square root of a perfect square is an integer, so for an irrational square root (m) is not a perfect square. In exams identifying perfect squares is important.

Step 3

Exam Tip

पूर्ण वर्ग का वर्गमूल पूर्णांक होता है, इसलिए अपरिमेय वर्गमूल के लिए (m) पूर्ण वर्ग नहीं होगा। परीक्षा में पूर्ण वर्ग पहचानना जरूरी है।

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Question 2/3 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

कौन सा मान (n) के लिए \(\sqrt{n}\) अपरिमेय है?

For which value of (n) is \(\sqrt{n}\) irrational?

Explanation opens after your attempt
Correct Answer

C. (n=98)

Step 1

Concept

(98) is not a perfect square, so \(\sqrt{98}=7\sqrt{2}\) is irrational. In exams extract perfect-square factors.

Step 2

Why this answer is correct

The correct answer is C. (n=98). (98) is not a perfect square, so \(\sqrt{98}=7\sqrt{2}\) is irrational. In exams extract perfect-square factors.

Step 3

Exam Tip

(98) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{98}=7\sqrt{2}\) अपरिमेय है। परीक्षा में पूर्ण वर्ग गुणनखंड निकालें।

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Question 3/3 Expert Mathematics Real Numbers Irrational numbers Class 10 Level 14

किस विकल्प में \(\sqrt{p}\) अपरिमेय है और (p) अभाज्य भी है?

In which option is \(\sqrt{p}\) irrational and (p) also prime?

Explanation opens after your attempt
Correct Answer

A. (p=11)

Step 1

Concept

(11) is a prime number.

Step 2

Why this answer is correct

A prime number is not a perfect square, so \(\sqrt{11}\) is irrational.

Step 3

Exam Tip

For the square root of a prime, use the non-perfect-square idea directly. चरण 1: (11) अभाज्य संख्या है। चरण 2: कोई अभाज्य संख्या पूर्ण वर्ग नहीं होती, इसलिए \(\sqrt{11}\) अपरिमेय है। चरण 3: अभाज्य संख्या के वर्गमूल पर सीधे अपूर्ण वर्ग का विचार लगाएँ।

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