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rational product MCQ Questions for Class 10

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4 questions tagged with rational product.

Question 1/4 Expert Mathematics Real Numbers Irrational numbers Class 10 Level 14

कौन-सा विकल्प \(3+\sqrt{2}\) और \(3-\sqrt{2}\) के बारे में सही है?

Which option is correct about \(3+\sqrt{2}\) and \(3-\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. दोनों अपरिमेय हैं और उनका गुणनफल परिमेय हैBoth are irrational and their product is rational

Step 1

Concept

\(3+\sqrt{2}\) and \(3-\sqrt{2}\) both contain an irrational part, so both are irrational.

Step 2

Why this answer is correct

Their product is (9-2=7), which is rational.

Step 3

Exam Tip

Conjugate irrational numbers can have a rational product. चरण 1: \(3+\sqrt{2}\) और \(3-\sqrt{2}\) दोनों में अपरिमेय भाग है, इसलिए दोनों अपरिमेय हैं। चरण 2: उनका गुणनफल (9-2=7) परिमेय है। चरण 3: संयुग्मी अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।

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Question 2/4 Expert Mathematics Real Numbers Irrational numbers Class 10 Level 13

यदि \(x=\sqrt{2}+\sqrt{5}\) और \(y=\sqrt{5}-\sqrt{2}\), तो (xy) का मान क्या है?

If \(x=\sqrt{2}+\sqrt{5}\) and \(y=\sqrt{5}-\sqrt{2}\), what is the value of (xy)?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

View the product as (\(\sqrt{5}+\sqrt{2}\)\(\sqrt{5}-\sqrt{2}\)).

Step 2

Why this answer is correct

It gives (5-2=3).

Step 3

Exam Tip

You can rearrange the order of addition to recognize a conjugate form. चरण 1: गुणन को (\(\sqrt{5}+\sqrt{2}\)\(\sqrt{5}-\sqrt{2}\)) की तरह देखें। चरण 2: यह (5-2=3) देता है। चरण 3: जोड़ के क्रम को बदलकर संयुग्मी रूप पहचान सकते हैं।

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Question 3/4 Hard Mathematics Real Numbers Irrational numbers Class 10 Level 15

यदि \(a=5+\sqrt{7}\) और \(b=5-\sqrt{7}\), तो (ab) का मान क्या है?

If \(a=5+\sqrt{7}\) and \(b=5-\sqrt{7}\), what is the value of (ab)?

Explanation opens after your attempt
Correct Answer

A. (18)

Step 1

Concept

This is multiplication of conjugates.

Step 2

Why this answer is correct

(ab=52-\(\sqrt{7}\)2=25-7=18).

Step 3

Exam Tip

In conjugate multiplication, the middle irrational terms cancel. चरण 1: यह संयुग्मी संख्याओं का गुणन है। चरण 2: (ab=52-\(\sqrt{7}\)2=25-7=18)। चरण 3: संयुग्मी गुणन में बीच के अपरिमेय पद कट जाते हैं।

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Question 4/4 Hard Mathematics Real Numbers Irrational numbers Class 10 Level 14

यदि \(a=\sqrt{3}+2\) और \(b=\sqrt{3}-2\), तो (ab) की प्रकृति क्या है?

If \(a=\sqrt{3}+2\) and \(b=\sqrt{3}-2\), what is the nature of (ab)?

Explanation opens after your attempt
Correct Answer

A. परिमेय और ऋणात्मकRational and negative

Step 1

Concept

(a) and (b) are conjugates.

Step 2

Why this answer is correct

(ab=\(\sqrt{3}\)2-22=3-4=-1), which is rational and negative.

Step 3

Exam Tip

In conjugate multiplication, the middle irrational terms cancel. चरण 1: (a) और (b) संयुग्मी रूप में हैं। चरण 2: (ab=\(\sqrt{3}\)2-22=3-4=-1), जो परिमेय और ऋणात्मक है। चरण 3: संयुग्मी गुणन में बीच के अपरिमेय पद कट जाते हैं।

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