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surd addition MCQ Questions for Class 10

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4 questions tagged with surd addition.

Question 1/4 Hard Mathematics Polynomials Representing real numbers on the number line Class 10 Level 49

संख्या रेखा पर \(\sqrt{2}+\sqrt{3}\) किस अंतराल में होगा?

On the number line, in which interval will \(\sqrt{2}+\sqrt{3}\) lie?

Explanation opens after your attempt
Correct Answer

A. ((3,4))

Step 1

Concept

\(\sqrt{2}\approx1.414\) and \(\sqrt{3}\approx1.732\), so the sum is about (3.146). Add approximate values for sums.

Step 2

Why this answer is correct

The correct answer is A. ((3,4)). \(\sqrt{2}\approx1.414\) and \(\sqrt{3}\approx1.732\), so the sum is about (3.146). Add approximate values for sums.

Step 3

Exam Tip

\(\sqrt{2}\approx1.414\) और \(\sqrt{3}\approx1.732\), इसलिए योग लगभग (3.146) है। योग के लिए अनुमानित मान जोड़ें।

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Question 2/4 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

किस विकल्प में \(\sqrt{3}\) और \(\sqrt{12}\) का योग परिमेय गुणांक वाले सरल अपरिमेय रूप में सही लिखा गया है?

In which option is the sum of \(\sqrt{3}\) and \(\sqrt{12}\) correctly written as a simple irrational form with rational coefficient?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

\(\sqrt{12}=2\sqrt{3}\), so \(\sqrt{3}+\sqrt{12}=3\sqrt{3}\). In exams make radicals like terms before adding.

Step 2

Why this answer is correct

The correct answer is A. \(3\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\), so \(\sqrt{3}+\sqrt{12}=3\sqrt{3}\). In exams make radicals like terms before adding.

Step 3

Exam Tip

\(\sqrt{12}=2\sqrt{3}\), इसलिए \(\sqrt{3}+\sqrt{12}=3\sqrt{3}\) है। परीक्षा में मूलों को जोड़ने से पहले समान मूल बनाएं।

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Question 3/4 Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

कौन सा व्यंजक परिमेय संख्या नहीं है?

Which expression is not a rational number?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{20}+\sqrt{45}\)

Step 1

Concept

\(\sqrt{20}+\sqrt{45}=2\sqrt{5}+3\sqrt{5}=5\sqrt{5}\), which is irrational. In exams do not treat addition like multiplication.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{20}+\sqrt{45}\). \(\sqrt{20}+\sqrt{45}=2\sqrt{5}+3\sqrt{5}=5\sqrt{5}\), which is irrational. In exams do not treat addition like multiplication.

Step 3

Exam Tip

\(\sqrt{20}+\sqrt{45}=2\sqrt{5}+3\sqrt{5}=5\sqrt{5}\), जो अपरिमेय है। परीक्षा में योग को गुणन जैसा न मानें।

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Question 4/4 Hard Mathematics Real Numbers Irrational numbers Class 10 Level 15

यदि \(x=\sqrt{6}+\sqrt{24}\), तो (x) किसके बराबर है?

If \(x=\sqrt{6}+\sqrt{24}\), what is (x) equal to?

Explanation opens after your attempt
Correct Answer

B. \(3\sqrt{6}\)

Step 1

Concept

\(\sqrt{24}=2\sqrt{6}\).

Step 2

Why this answer is correct

So \(x=\sqrt{6}+2\sqrt{6}=3\sqrt{6}\), which is irrational.

Step 3

Exam Tip

Simplify radicals to like terms before adding. चरण 1: \(\sqrt{24}=2\sqrt{6}\) है। चरण 2: इसलिए \(x=\sqrt{6}+2\sqrt{6}=3\sqrt{6}\), जो अपरिमेय है। चरण 3: मूल को सरल करके समान पद बनाएँ, फिर जोड़ें।

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