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

NCERT exercise solutions help improve the hold of the students in the problems related to square and square roots. Subject experts have solved all the questions of this exercise. NCERT Solutions for Class 8 Maths helps students in enhancing their skills. Download free Maths NCERT Solutions for Chapter 6 of Class 8 and get going with the homework as well as the exam preparation.

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Access other exercise solutions of Class 8 Maths Chapter 6 – Squares and Square Roots

Exercise 6.1 Solutions 9 Questions

Exercise 6.2 Solutions 2 Questions

Exercise 6.3 Solutions 10 Questions

Access answers of Maths NCERT Class 8 Chapter 6 – Squares and Square Roots Exercise 6.4 Page Number 107

1. Find the square root of each of the following numbers by the 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:

i.

∴ √2304 = 48

ii.

∴ √4489 = 67

iii.

∴ √3481 = 59

iv.

∴ √529 = 23

v.

∴ √3249 = 57

vi.

∴ √1369 = 37

vii.

∴ √5776 = 76

viii.

∴ √7921 = 89

ix.

∴ √576 = 24

x.

∴ √1024 = 32

xi.

∴ √3136 = 56

xii.

∴ √900 = 30

2. Find the number of digits in the square root of each of the following numbers (without any

calculation).

i. 144

ii. 4489

iii. 27225

iv. 390625

Solution:

i.

∴ √144 = 12

Hence, the square root of the number 144 has 2 digits.

ii.

∴ √4489 = 67

Hence, the square root of the number 4489 has 2 digits.

iii.

√27225 = 165

Hence, the square root of the number 27225 has 3 digits.

iv.

∴ √390625 = 625

Hence, the square root of the number 390625 has 3 digits.

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 = 1.6

ii.

∴ √7.29 = 2.7

iii.

∴ √51.84 = 7.2

iv.

∴ √42.25 = 6.5

v.

∴ √31.36 = 5.6

4. Find the least number which must be subtracted from each of the following numbers 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 = 20

∴ we must subtract 2 from 402 to get a perfect square.

New number = 402 – 2 = 400

∴ √400 = 20

ii.

∴ We must subtract 53 from 1989 to get a perfect square. New number = 1989 – 53 = 1936

∴ √1936 = 44

iii.

∴ We must subtract 1 from 3250 to get a perfect square.

New number = 3250 – 1 = 3249

∴ √3249 = 57

iv.

We must subtract 41 from 825 to get a perfect square.

New number = 825 – 41 = 784

∴ √784 = 28

∴ we must subtract 31 from 4000 to get a perfect square. New number = 4000 – 31 = 3969

∴ √3969 = 63

5. Find the least number which must be added to each of the following numbers 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)

Here, (22)2 < 525 > (23)2

We can say 525 is ( 129 – 125 ) 4 less than (23)2.

∴ if we add 4 to 525, it will be a perfect square. New number = 525 + 4 = 529

∴ √529 = 23

(ii)

Here, (41)2 < 1750 > (42)²

We can say 1750 is ( 164 – 150 ) 14 less than (42)².

∴ If we add 14 to 1750, it will be a perfect square.

New number = 1750 + 14 = 1764

∴√1764 = 42

(iii)

Here, (15)2 < 252 > (16)2

We can say 252 is ( 156 – 152 ) 4 less than (16)2.

∴ if we add 4 to 252, it will be a perfect square.

New number = 252 + 4 = 256

∴ √256 = 16

(iv)

Here, (42)2 < 1825 > (43)2

We can say 1825 is ( 249 – 225 ) 24 less than (43)2.

∴ if we add 24 to 1825, it will be a perfect square.

New number = 1825 + 24 = 1849

∴ √1849 = 43

(v)

Here, (80)2 < 6412 > (81)2

We can say 6412 is ( 161 – 12 ) 149 less than (81)2.

∴ if we add 149 to 6412, it will be a perfect square.

New number = 6412 + 149 = 656

∴ √6561 = 81

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

Solution:

Let the length of each side of the field = a Then, the area of the field = 441 m2

⇒ a2 = 441 m2

⇒a = √441 m

∴ The length of each side of the field = a m = 21 m.

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.

Given, AB = 6 cm, BC = 8 cm

Let AC be x cm.

∴ AC2 = AB2 + BC2

Hence, AC = 10 cm.

b.

Given, AC = 13 cm, BC = 5 cm

Let AB be x cm.

∴ AC2 = AB2 + BC2

⇒ AC2 – BC2 = AB2

Hence, AB = 12 cm

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 remains the same. Find the minimum number of plants he needs for this.

Solution:

Let the number of rows and columns be x.

∴ The total number of rows and columns= x× x = x2 As per the question, x2 = 1000

⇒ x = √1000

Here, (31)2 < 1000 > (32)2

We can say 1000 is ( 124 – 100 ) 24 less than (32)2.

∴ 24 more plants are needed.

9. There are 500 children in a school. For a P.T. drill, they have to stand so that the number of rows is equal to the number of columns. How many children would be left out in this arrangement?

Solution:

Let the number of rows and columns be x.

∴ The total number of rows and columns = x × x = x2 As per question, x2 = 500

x = √500

Hence, 16 children would be left out of the arrangement.

Exercise 6.4 of NCERT Solutions for Class 8 Maths Chapter 6 – Squares and Square Roots is based on the following topics:

1. Finding the square root by division method
2. Square Roots of Decimals
3. Estimating Square Root

Also, explore – 

NCERT Solutions for Class 8 Maths

NCERT Solutions for Class 8