Class 9 Mathematics - Number Systems - Square root spiral Easy Quiz

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एक वर्ग की भुजा \(\sqrt{7}\) इकाई है। उसका परिमाप किस प्रकार की संख्या होगा?

The side of a square is \(\sqrt{7}\) units. What type of number will its perimeter be?

Explanation opens after your attempt
Correct Answer

B. अपरिमेय संख्याIrrational number

Step 1

Concept

The perimeter is \(4\sqrt{7}\) and \(\sqrt{7}\) is irrational. A non-zero rational multiplier keeps irrationality.

Step 2

Why this answer is correct

The correct answer is B. अपरिमेय संख्या / Irrational number. The perimeter is \(4\sqrt{7}\) and \(\sqrt{7}\) is irrational. A non-zero rational multiplier keeps irrationality.

Step 3

Exam Tip

परिमाप \(4\sqrt{7}\) होगा और \(\sqrt{7}\) अपरिमेय है। शून्येतर परिमेय गुणक से अपरिमेयता बनी रहती है।

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यदि किसी वर्ग का क्षेत्रफल (11) वर्ग इकाई है तो उसकी भुजा किस प्रकार की संख्या होगी?

If the area of a square is (11) square units then what type of number will its side be?

Explanation opens after your attempt
Correct Answer

D. अपरिमेय संख्याIrrational number

Step 1

Concept

The side will be \(\sqrt{11}\) and (11) is not a perfect square. So \(\sqrt{11}\) is irrational.

Step 2

Why this answer is correct

The correct answer is D. अपरिमेय संख्या / Irrational number. The side will be \(\sqrt{11}\) and (11) is not a perfect square. So \(\sqrt{11}\) is irrational.

Step 3

Exam Tip

भुजा \(\sqrt{11}\) होगी और (11) पूर्ण वर्ग नहीं है। इसलिए \(\sqrt{11}\) अपरिमेय है।

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इनमें से कौन-सा वर्गमूल अपरिमेय नहीं है?

Which square root is not irrational?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{64}\)

Step 1

Concept

\(\sqrt{64}=8\) so it is rational. Square roots of perfect squares are not irrational.

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{64}\). \(\sqrt{64}=8\) so it is rational. Square roots of perfect squares are not irrational.

Step 3

Exam Tip

\(\sqrt{64}=8\) इसलिए यह परिमेय है। पूर्ण वर्गों के वर्गमूल अपरिमेय नहीं होते।

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यदि एक वर्ग की भुजा \(\sqrt{3}\) इकाई है तो उसका क्षेत्रफल क्या होगा?

If the side of a square is \(\sqrt{3}\) units, what will be its area?

Explanation opens after your attempt
Correct Answer

A. (3) वर्ग इकाई(3) square units

Step 1

Concept

The area is (\(\sqrt{3}\)2=3). A square with irrational side can have rational area.

Step 2

Why this answer is correct

The correct answer is A. (3) वर्ग इकाई / (3) square units. The area is (\(\sqrt{3}\)2=3). A square with irrational side can have rational area.

Step 3

Exam Tip

क्षेत्रफल (\(\sqrt{3}\)2=3) है। अपरिमेय भुजा का क्षेत्रफल परिमेय हो सकता है।

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किस संख्या का वर्ग (19) है और वह धनात्मक है?

Which number has square (19) and is positive?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{19}\)

Step 1

Concept

The positive number is \(\sqrt{19}\) because (\(\sqrt{19}\)2=19). Since (19) is not a perfect square, it is irrational.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{19}\). The positive number is \(\sqrt{19}\) because (\(\sqrt{19}\)2=19). Since (19) is not a perfect square, it is irrational.

Step 3

Exam Tip

धनात्मक संख्या \(\sqrt{19}\) है क्योंकि (\(\sqrt{19}\)2=19)। (19) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है।

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यदि किसी धनात्मक संख्या का वर्ग (37) है, तो वह संख्या कौन-सी होगी?

If the square of a positive number is (37), which number is it?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{37}\)

Step 1

Concept

The positive number is \(\sqrt{37}\) because (\(\sqrt{37}\)2=37). Since (37) is not a perfect square, it is irrational.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{37}\). The positive number is \(\sqrt{37}\) because (\(\sqrt{37}\)2=37). Since (37) is not a perfect square, it is irrational.

Step 3

Exam Tip

धनात्मक संख्या \(\sqrt{37}\) है क्योंकि (\(\sqrt{37}\)2=37)। (37) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है।

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