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

Squares and Square Roots

Question 1.
Find the square root of each of the following numbers by Division method :
(i)
 2304
(ii) 4489
(iii) 3481
(iv) 529
(v) 3249
(vi) 1369
(vii) 5776
(viii) 7921
(ix) 576
(x) 1024
(xi) 3136
(xii) 900

Solution:
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 20
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 21
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 22
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 23
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 24
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 25

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:
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 26

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) Here, the number of decimal places is already even. So, mark off periods and proceed as under :
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 27
∴ \sqrt { 2.56 } =1.6

(ii) Here, the number of decimal places are already even. So, mark off periods and proceed as under :
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 28
∴ \sqrt { 7.29 } =2.7

(iii) Here, the number of decimal places are already even. So, mark off periods and proceed as under :
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 29
∴ \sqrt { 51.84 } =7.2

(iv) Here, the number of decimal places are already even. So, mark off periods and proceed as under :
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 30
∴ \sqrt { 42.25 } =6.5

(v) Here, the number of decimal places are already even. So, mark off periods and proceed as under :
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 31
∴ \sqrt { 31.36 } =5.6

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) Let us try to find the square root of 402.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 32
This shows the (20)2 is less than 402 by 2. So, in order to get a perfect square, 2 must be subtracted from the given number.
∴ Required perfect square number = 402 – 2 = 400
Also, \sqrt { 400 } =20

(ii) Let us try to find the square root of 1989.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 33
This shows that (44)2 is less than 1989 by 53. So, in order to get a perfect square, 53 must be subtracted from the given number.
∴ Required perfect square number = 1989 – 53 = 1936
Also, \sqrt { 1936 } =44

(iii) Let us try to find the square root of 3250.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 34
This shows that (57)2 is less than 3250 by 1. So, in order to get a perfect square, 1 must be subtracted from the given number.
∴ Required perfect number = 3250 -1 = 3249
Also, \sqrt { 3249 } =57

(iv) Let us try to find the square root of 825.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 35
This shows that (28)2 is less than 825 by 41. So, in order to get a perfect square, 41 must be subtracted from the given number.
∴ Required perfect square number = 825 – 41 = 784
Also, \sqrt { 784 } =28

(v) Let us try to find the square root of 4000.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 36
This shows that (63)2 is less than 4000 by 31. So, in order to get a perfect square, 31 must be subtracted from the given number.
∴ Required perfect square number = 4000 – 31 = 3969
Also, \sqrt { 3969 } =63

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) We try to find out the square root of 525.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 37

(ii) We try to find out the square root of 1750.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 38

(iii) We try to find out the square root of 252.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 39
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 40

(iv) We try to find out the square root of 1825.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 41

(v) We try to find out the square root of 6412.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 42

Question 6.
Find the length of the side of a square whose area is 441 m2.

Solution:
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 43

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:
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 44

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 us find the square root of 1000.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 45
This shows that (31)2 is less than 1000 by 39 and (32)2 =1024. Thus, the gardener needs 1024 -1000 = 24 plants more to plant in such a way that the number of rows and the number of columns remain the same.

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 us find the square root of 500.
This shows that (22)2 = 484 is less than 500 by 16.
∴ 16 students have to go out for others to do the P.T. practice as per condition.
NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 46

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