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irrational between integers MCQ Questions for Class 10

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2 questions tagged with irrational between integers.

Question 1/2 Expert Mathematics Real Numbers Irrational numbers Class 10 Level 14

कौन-सा विकल्प (2) और (3) के बीच दो अपरिमेय संख्याओं का सही युग्म है?

Which option is a correct pair of two irrational numbers between (2) and (3)?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{5},\sqrt{8}\)

Step 1

Concept

\(2=\sqrt{4}\) and \(3=\sqrt{9}\).

Step 2

Why this answer is correct

(5) and (8) lie between (4) and (9) and are not perfect squares. Therefore \(\sqrt{5}\) and \(\sqrt{8}\) are irrational numbers between (2) and (3).

Step 3

Exam Tip

Non-perfect squares between two square numbers give such pairs. चरण 1: \(2=\sqrt{4}\) और \(3=\sqrt{9}\) हैं। चरण 2: (5) और (8) दोनों (4) और (9) के बीच हैं तथा पूर्ण वर्ग नहीं हैं। इसलिए \(\sqrt{5}\) और \(\sqrt{8}\) दोनों अपरिमेय हैं और (2) से (3) के बीच हैं। चरण 3: बीच के अपूर्ण वर्गों से ऐसे युग्म बनते हैं।

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Question 2/2 Hard Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सी संख्या (3) और (4) के बीच एक अपरिमेय संख्या है?

Which number is an irrational number between (3) and (4)?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{10}\)

Step 1

Concept

\(3=\sqrt{9}\) and \(4=\sqrt{16}\).

Step 2

Why this answer is correct

(10) is not a perfect square and (9<10<16), so \(\sqrt{10}\) is an irrational number between (3) and (4).

Step 3

Exam Tip

A non-perfect square between two square numbers helps find an irrational number between two integers. चरण 1: \(3=\sqrt{9}\) और \(4=\sqrt{16}\) हैं। चरण 2: (10) पूर्ण वर्ग नहीं है और (9<10<16), इसलिए \(\sqrt{10}\) (3) और (4) के बीच अपरिमेय संख्या है। चरण 3: दो पूर्णांकों के बीच अपरिमेय खोजने में बीच का अपूर्ण वर्ग उपयोगी होता है।

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