Square Roots

Author:Subject Experts

8th CBSE

IMPORTANT

Important Questions on Square Roots

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 1

Find the smallest square number that is divisible by each of the numbers $8, 15$ and $20$ . Also, find the square root of the result.

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 2

Find the least number that must be added to $1700$ , to get a perfect square. Also, find the square root of the result.

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 3

Find the smallest number by which $9408$ must be divided, so that quotient is a perfect square. Find the square root of the quotient.

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 4

Find the square root of $11.56$ by division method.

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 5

Find the square root of $6.76$ by division method.

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 6

Find the square root of $2025$ by division method.

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 7

Find the square root of the following by division method.

$484$

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 8

A general wishing to arrange his men, who were $335250$ in number in the form of a square found that there were $9$ men left over. How many were there in each row?

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 9

The area of a square field is $101 \frac{1}{400} sq m$ . Find the length of one side of the field in decimals.

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 10

During a mass drill exercise $6250$ students of different schools were arranged in rows such that the number of students in each row was equal to the number of rows. In doing so,the instructor found out that $9$ children were left out. Find the number of children in each row.

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 11

If the area of a square is $38.44 sq cm$ , then find the side of the square.

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 12

Find the least number by which $216$ must be divided to make the result a perfect square.

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 13

Find the value of $\sqrt{0.0081}$

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 14

Simplify: $\sqrt{15612 + \sqrt{154 + \sqrt{225}}}$ .

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 15

If $\sqrt{2401} = \sqrt{7^{x}}$ , then the value of $x$ .

HARD

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 16

Complete the following table

S. No.	Number	Prime Factors	Smallest number by which number should be divided to make a perfect square
(i)	$2700$	$2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5$	$3, [2700 \div 3 = 900]$
(ii)	$1620$	---------	----------
(iii)	$14175$	---------	----------
(iv)	$25857$	---------	----------

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 17

In a right angled $∆ P Q R, ∠ Q = 90 °, P Q = 6 cm$ and $Q R = 8 cm$ . If $P R = k cm$ , then find the value of $k$ .

MEDIUM

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 18

$2025$ plants to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the sum of the number of rows and the number of plants in row.

HARD

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 19

Complete the following table

S. No.	Number	Prime Factors	Smallest number to be multiplied to make the given number a perfect square
(i)	$2700$	$2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5$	$3, [2700 \times 3 = 8100]$
(ii)	$1575$	---------	----------
(iii)	$1620$	---------	----------
(iv)	$11200$	---------	----------

EASY

IMPORTANT

NCERT Practice Workbook Mathematics>Squares and Square Roots>Square Roots> Q 20

Find the factors of the number and identify the prime factor which is not paired.

S. No.

Number

Finding the prime factors

Prime factors

(i)

48

$2 \times 2 \times 2 \times 2 \times 3$

$3$ is not paired

(ii)

27

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Square Roots

Important Questions on Square Roots

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