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2 results found for "surd expressions" in Class 10.

Question Expert Mathematics Chapter 1: Real Numbers 5: Irrational numbers Class 10 Level 14

कौन-सा विकल्प \(\sqrt{2}+\sqrt{18}-\sqrt{50}+\sqrt{98}\) का सही सरल रूप है?

Which option is the correct simplified form of \(\sqrt{2}+\sqrt{18}-\sqrt{50}+\sqrt{98}\)?

Explanation opens after your attempt
Correct Answer

A. \(6\sqrt{2}\)

Step 1

Concept

\(\sqrt{18}=3\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), and \(\sqrt{98}=7\sqrt{2}\).

Step 2

Why this answer is correct

\(1\sqrt{2}+3\sqrt{2}-5\sqrt{2}+7\sqrt{2}=6\sqrt{2}\).

Step 3

Exam Tip

In long surd expressions, write the coefficients separately and add them. चरण 1: \(\sqrt{18}=3\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), और \(\sqrt{98}=7\sqrt{2}\)। चरण 2: \(1\sqrt{2}+3\sqrt{2}-5\sqrt{2}+7\sqrt{2}=6\sqrt{2}\)। चरण 3: लंबे मूल वाले प्रश्न में गुणांक अलग लिखकर जोड़ना आसान रहता है।

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Question Hard Mathematics Chapter 1: Real Numbers 5: Irrational numbers Class 10 Level 15

निम्न में से कौन-सा व्यंजक परिमेय नहीं है?

Which of the following expressions is not rational?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{6}+\sqrt{24}\)

Step 1

Concept

Simplify each option first.

Step 2

Why this answer is correct

\(\sqrt{6}+\sqrt{24}=\sqrt{6}+2\sqrt{6}=3\sqrt{6}\), which is irrational.

Step 3

Exam Tip

Radicals may cancel in multiplication, but not always in addition. चरण 1: पहले प्रत्येक विकल्प को सरल करें। चरण 2: \(\sqrt{6}+\sqrt{24}=\sqrt{6}+2\sqrt{6}=3\sqrt{6}\), जो अपरिमेय है। चरण 3: गुणन में मूल कट सकते हैं, पर योग में हमेशा ऐसा नहीं होता।

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