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irrational-expression MCQ Questions for Class 10

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33 questions tagged with irrational-expression.

Question 31/33 Medium Mathematics Real Numbers Irrational numbers Class 10 Level 13

\(\sqrt{3}+\sqrt{12}+\sqrt{27}\) की प्रकृति क्या है?

What is the nature of \(\sqrt{3}+\sqrt{12}+\sqrt{27}\)?

Explanation opens after your attempt
Correct Answer

B. अपरिमेयIrrational

Step 1

Concept

\(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\).

Step 2

Why this answer is correct

The total is \(6\sqrt{3}\), which is irrational.

Step 3

Exam Tip

Decide the nature of the number only after simplification. चरण 1: \(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\)। चरण 2: कुल योग \(6\sqrt{3}\) है, जो अपरिमेय है। चरण 3: सरलीकरण के बाद ही संख्या की प्रकृति तय करें।

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Question 32/33 Medium Mathematics Real Numbers Irrational numbers Class 10 Level 13

(\left\(\sqrt{5}+2\right\)2) का मान क्या है?

What is the value of (\left\(\sqrt{5}+2\right\)2)?

Explanation opens after your attempt
Correct Answer

A. \(9+4\sqrt{5}\)

Step 1

Concept

Use ((a+b)2=a-2+2ab+b-2).

Step 2

Why this answer is correct

(\(\sqrt{5}\)2+2\(\sqrt{5}\)(2)+22=5+4\sqrt{5}+4=9+4\sqrt{5}).

Step 3

Exam Tip

Missing the middle term (2ab) is a common mistake. चरण 1: ((a+b)2=a-2+2ab+b-2) लगाएं। चरण 2: (\(\sqrt{5}\)2+2\(\sqrt{5}\)(2)+22=5+4\sqrt{5}+4=9+4\sqrt{5})। चरण 3: मध्य पद (2ab) को छोड़ना सामान्य गलती है।

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Question 33/33 Medium Mathematics Real Numbers Irrational numbers Class 10 Level 13

यदि \(x=3+\sqrt{5}\), तो (x-3) किस प्रकार की संख्या है?

If \(x=3+\sqrt{5}\), what type of number is (x-3)?

Explanation opens after your attempt
Correct Answer

B. अपरिमेयIrrational

Step 1

Concept

(x-3=\(3+\sqrt{5}\)-3).

Step 2

Why this answer is correct

This leaves \(\sqrt{5}\), which is irrational.

Step 3

Exam Tip

Simplify the expression before deciding the nature of the number. चरण 1: (x-3=\(3+\sqrt{5}\)-3) होगा। चरण 2: इससे \(\sqrt{5}\) बचता है, जो अपरिमेय है। चरण 3: अभिव्यक्ति को सरल करके संख्या की प्रकृति तय करें।

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