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2 results found for "rational quotient" in Class 10.

Question Expert Mathematics Chapter 1: Real Numbers 5: Irrational numbers Class 10 Level 13

किस विकल्प में \(\frac{\sqrt{a}}{\sqrt{b}}\) अपरिमेय है?

In which option is \(\frac{\sqrt{a}}{\sqrt{b}}\) irrational?

Explanation opens after your attempt
Correct Answer

B. (a=50,b=2)

Step 1

Concept

\(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\).

Step 2

Why this answer is correct

For (a=50,b=2), it becomes \(\sqrt{25}=5\), which is rational, so it should not be selected.

Step 3

Exam Tip

For an irrational quotient, \(\frac{a}{b}\) should not be a perfect square; none of the listed options gives that. चरण 1: \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\) है। चरण 2: (a=50,b=2) पर \(\sqrt{\frac{50}{2}}=\sqrt{25}=5\), यह परिमेय है; इसलिए इसे नहीं चुनना चाहिए। चरण 3: सही अपरिमेय के लिए भागफल पूर्ण वर्ग न हो, जैसे यहाँ दिए विकल्पों में कोई अपरिमेय परिणाम नहीं बनता।

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

यदि \(y=\sqrt{8}+\sqrt{32}\), तो \(\frac{y}{\sqrt{2}}\) का मान क्या है?

If \(y=\sqrt{8}+\sqrt{32}\), what is the value of \(\frac{y}{\sqrt{2}}\)?

Explanation opens after your attempt
Correct Answer

A. (6)

Step 1

Concept

\(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{32}=4\sqrt{2}\).

Step 2

Why this answer is correct

\(y=6\sqrt{2}\), so \(\frac{y}{\sqrt{2}}=6\).

Step 3

Exam Tip

First add like surds, then divide. चरण 1: \(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\)। चरण 2: \(y=6\sqrt{2}\), इसलिए \(\frac{y}{\sqrt{2}}=6\)। चरण 3: पहले समान मूल वाले पदों को जोड़ें, फिर भाग दें।

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