NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4

NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 6
Chapter Name Squares and Square Roots
Exercise Ex 6.4
Number of Questions Solved 9
Category NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4

Question 1.
Find the square root of each of the following numbers by Division method:
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 1
Solution.
(i) 2304
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 2

(ii) 4489
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 3

(iii) 3481
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 4

(iv) 529
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 5

(v) 3249
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 6

(vi) 1369
(vii) 5776
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 8

(viii) 7921
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 9

(ix) 576
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 10

(x) 1024
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(xi) 3136
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 12

(xii) 900
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 13

Question 2.
Find the number of digits in the square root of each of the following numbers (without any calculation):
(i) 64
(ii) 144
(iii) 4489
(iv) 27225
(v) 390625.
Solution.
(i) 64
Number (n) of digits in 64 = 2 which is even.
∴ Number of digits in the square root of 64 \(\frac { n }{ 2 } =\frac { 2 }{ 2 } =1\)

(ii) 144
Number (n) of digits in 144 = 3 which is
∴ Number of digits in the square root of 144 \(\frac { n+1 }{ 2 } =\frac { 3+1 }{ 2 } =\frac { 4 }{ 2 } =2\)

(iii) 4489
Number (n) of digits in 4489 = 4 which is even.
∴ Number of digits in the square root of 4489 \(\frac { n }{ 2 } =\frac { 4 }{ 2 } =2\)

(iv) 27225
Number (n) of digits in 27225 = 5 which is odd.
∴ Number of digits in the square root of 27225 \(\frac { n+1 }{ 2 } =\frac { 5+1 }{ 2 } =\frac { 6 }{ 2 } =3\)

(v) 390625
Number (n) of digits in 390625 = 6 which is even.
∴ Number of digits in the square root of 390625 \(\frac { n }{ 2 } =\frac { 6 }{ 2 } =3\)

Question 3.
Find the square root of the following decimal numbers:
(i) 2.56
(ii) 7.29
(iii) 51.84
(iv) 42.25
(v) 31.36
Solution.
(i) 2.56
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 14

(ii) 7.29
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 15

(iii) 51.84
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 16

(iv) 42.25
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 17

(v) 31.36
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 18

Question 4.
Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.
(i) 402
(ii) 1989
(iii) 3250
(iv) 825
(v) 4000
Solution.
(i)402
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 19
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 20

(ii) 1989
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 21

(iii) 3250
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 22

(iv) 825
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 23

(v) 4000
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 24

Question 5.
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.
(i) 525
(ii) 1750
(iii) 252
(iv) 1825
(v) 6412
Solution.
(i) 525
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 25

(ii) 1750
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 26

(iii) 252
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 27
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 28

(iv) 1825
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 29

(v) 6412
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 30

Question 6.
Find the length of the side of a square whose area is 441 \({ m }^{ 2 }\).
Solution.
Area of the square = 441 \({ m }^{ 2 }\)
∴ Length of the side of the square
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 31

Question 7.
In a right triangle ABC, ∠B = 90°.
(a) If AB = 6 cm, BC = 8 cm, find AC
(b) If AC 13 cm, BC = 5 cm, find AB.
Solution.
(a) In the right triangle ABC,
∠B = 90°
Given
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 32
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 33
NCERTa Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.3 33

Question 8.
A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.
Solution.
Let the number of rows be x.
Then the number of columns is x.
NCERTa Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.3 34

Question 9.
There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?
Solution.
Let the number of rows be x.
Then the number of columns is x.
NCERTa Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.3 35

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