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surd MCQ Questions for Class 10

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

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5 questions tagged with surd.

Question 1/5 Hard Mathematics Polynomials Representing real numbers on the number line Class 10 Level 49

संख्या रेखा पर \(\sqrt{50}\) को सरल कर अनुमान लगाने पर वह किसके निकट है?

After simplifying and estimating \(\sqrt{50}\) on the number line, it is near which value?

Explanation opens after your attempt
Correct Answer

A. (7.07)

Step 1

Concept

\(\sqrt{50}=5\sqrt{2}\approx5\times1.414=7.07\). First take out the largest perfect-square factor.

Step 2

Why this answer is correct

The correct answer is A. (7.07). \(\sqrt{50}=5\sqrt{2}\approx5\times1.414=7.07\). First take out the largest perfect-square factor.

Step 3

Exam Tip

\(\sqrt{50}=5\sqrt{2}\approx5\times1.414=7.07\)। पहले बड़ा पूर्ण वर्ग बाहर निकालें।

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Question 2/5 Hard Mathematics Polynomials Representing real numbers on the number line Class 10 Level 49

संख्या रेखा पर \(\sqrt{2}\) और \(\sqrt{8}\) के मध्य बिंदु का मान क्या होगा?

What is the midpoint of \(\sqrt{2}\) and \(\sqrt{8}\) on the number line?

Explanation opens after your attempt
Correct Answer

A. \(\frac{3\sqrt{2}}{2}\)

Step 1

Concept

\(\sqrt{8}=2\sqrt{2}\), so the midpoint is \(\frac{\sqrt{2}+2\sqrt{2}}{2}=\frac{3\sqrt{2}}{2}\). Simplify first, then average.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{3\sqrt{2}}{2}\). \(\sqrt{8}=2\sqrt{2}\), so the midpoint is \(\frac{\sqrt{2}+2\sqrt{2}}{2}=\frac{3\sqrt{2}}{2}\). Simplify first, then average.

Step 3

Exam Tip

\(\sqrt{8}=2\sqrt{2}\), इसलिए मध्य बिंदु \(\frac{\sqrt{2}+2\sqrt{2}}{2}=\frac{3\sqrt{2}}{2}\) है। सरलीकरण के बाद औसत लें।

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Question 3/5 Hard Mathematics Polynomials Representing real numbers on the number line Class 10 Level 49

यदि (A) संख्या रेखा पर \(\sqrt{18}\) है, तो (A) किसके सबसे निकट होगा?

If (A) is \(\sqrt{18}\) on the number line, to which number is (A) closest?

Explanation opens after your attempt
Correct Answer

A. (4.24)

Step 1

Concept

\(\sqrt{18}=3\sqrt{2}\approx4.242\), so (4.24) is closest. Simplification makes estimation easier.

Step 2

Why this answer is correct

The correct answer is A. (4.24). \(\sqrt{18}=3\sqrt{2}\approx4.242\), so (4.24) is closest. Simplification makes estimation easier.

Step 3

Exam Tip

\(\sqrt{18}=3\sqrt{2}\approx4.242\), इसलिए (4.24) सबसे निकट है। सरलीकरण अनुमान को आसान बनाता है।

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Question 4/5 Hard Mathematics Polynomials Representing real numbers on the number line Class 10 Level 49

यदि \(x=\sqrt{12}\), तो संख्या रेखा पर (x) के लिए सही सरलीकृत रूप कौन-सा है?

If \(x=\sqrt{12}\), which simplified form is correct for placing (x) on the number line?

Explanation opens after your attempt
Correct Answer

A. \(2\sqrt{3}\)

Step 1

Concept

\(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\). Simplify the square root before estimating its position.

Step 2

Why this answer is correct

The correct answer is A. \(2\sqrt{3}\). \(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\). Simplify the square root before estimating its position.

Step 3

Exam Tip

\(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\)। स्थान अनुमान से पहले वर्गमूल को सरल करें।

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Question 5/5 Hard Mathematics Real Numbers Irrational numbers Class 10 Level 14

यदि \(x=\sqrt{5}-2\), तो (x) के बारे में सही कथन कौन-सा है?

If \(x=\sqrt{5}-2\), which statement about (x) is correct?

Explanation opens after your attempt
Correct Answer

B. (x) अपरिमेय है(x) is irrational

Step 1

Concept

\(\sqrt{5}\) is irrational and (2) is rational.

Step 2

Why this answer is correct

Subtracting a rational number from an irrational number gives an irrational number.

Step 3

Exam Tip

When an integer is subtracted from a surd, focus on the nature of the surd. चरण 1: \(\sqrt{5}\) अपरिमेय है और (2) परिमेय है। चरण 2: अपरिमेय संख्या में से परिमेय संख्या घटाने पर परिणाम अपरिमेय रहता है। चरण 3: किसी मूल से पूर्णांक घटाने पर भी मूल की प्रकृति पर ध्यान दें।

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