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

NCERT exercise solutions are helpful to improve the hold of the students in the problems related to square and square roots. All the questions of this exercise have been solved by subject experts. 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.

Download PDF of NCERT Solutions for class 8 Maths Chapter 6- Squares and Square Roots Exercise 6.4

 

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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 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.

NCERT Solution For Class 8 Maths Chapter 6 Image 37

∴ √2304 = 48

ii.

NCERT Solution For Class 8 Maths Chapter 6 Image 38

∴ √4489 = 67

iii.

NCERT Solution For Class 8 Maths Chapter 6 Image 39

∴ √3481 = 59

iv.

NCERT Solution For Class 8 Maths Chapter 6 Image 40

∴ √529 = 23

NCERT Solution For Class 8 Maths Chapter 6 Image 41v.

∴ √3249 = 57

vi.

NCERT Solution For Class 8 Maths Chapter 6 Image 42

∴ √1369 = 37

NCERT Solution For Class 8 Maths Chapter 6 Image 43vii.

∴ √5776 = 76

NCERT Solution For Class 8 Maths Chapter 6 Image 44viii.

∴ √7921 = 89

ix.

NCERT Solution For Class 8 Maths Chapter 6 Image 45

∴ √576 = 24

x.

NCERT Solution For Class 8 Maths Chapter 6 Image 46

∴ √1024 = 32

xi.

NCERT Solution For Class 8 Maths Chapter 6 Image 47

∴ √3136 = 56

xii.

NCERT Solution For Class 8 Maths Chapter 6 Image 48

∴ √900 = 30

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

calculation).64

i. 144

ii. 4489

iii. 27225

iv. 390625

Solution:

i.

NCERT Solution For Class 8 Maths Chapter 6 Image 49

∴ √144 = 12

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

ii.

NCERT Solution For Class 8 Maths Chapter 6 Image 50

∴ √4489 = 67

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

iii.
NCERT Solution For Class 8 Maths Chapter 6 Image 51

√27225 = 165

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

NCERT Solution For Class 8 Maths Chapter 6 Image 52iv.

∴ √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.

NCERT Solution For Class 8 Maths Chapter 6 Image 53

∴ √2.56 = 1.6

ii.

NCERT Solution For Class 8 Maths Chapter 6 Image 54

∴ √7.29 = 2.7

iii.

NCERT Solution For Class 8 Maths Chapter 6 Image 55

∴ √51.84 = 7.2

iv.

NCERT Solution For Class 8 Maths Chapter 6 Image 56

∴ √42.25 = 6.5

NCERT Solution For Class 8 Maths Chapter 6 Image 57v.

∴ √31.36 = 5.6

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.

NCERT Solution For Class 8 Maths Chapter 6 Image 58∴ √400 = 20

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

New number = 402 – 2 = 400

NCERT Solution For Class 8 Maths Chapter 6 Image 59

∴ √400 = 20

ii.

NCERT Solution For Class 8 Maths Chapter 6 Image 60

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

NCERT Solution For Class 8 Maths Chapter 6 Image 61

∴ √1936 = 44

iii.

NCERT Solution For Class 8 Maths Chapter 6 Image 62

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

New number = 3250 – 1 = 3249

NCERT Solution For Class 8 Maths Chapter 6 Image 63

∴ √3249 = 57

iv.

NCERT Solution For Class 8 Maths Chapter 6 Image 64

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

New number = 825 – 41 = 784

NCERT Solution For Class 8 Maths Chapter 6 Image 65

∴ √784 = 28

NCERT Solution For Class 8 Maths Chapter 6 Image 66

∴ 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 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)

NCERT Solution For Class 8 Maths Chapter 6 Image 67

NCERT Solution For Class 8 Maths Chapter 6 Image 68

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 perfect square. New number = 525 + 4 = 529

NCERT Solution For Class 8 Maths Chapter 6 Image 69

∴ √529 = 23

NCERT Solution For Class 8 Maths Chapter 6 Image 70(ii)

NCERT Solution For Class 8 Maths Chapter 6 Image 71

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 perfect square.

New number = 1750 + 14 = 1764

NCERT Solution For Class 8 Maths Chapter 6 Image 72

∴√1764 = 42

(iii)

NCERT Solution For Class 8 Maths Chapter 6 Image 73

NCERT Solution For Class 8 Maths Chapter 6 Image 74

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 perfect square.

New number = 252 + 4 = 256

NCERT Solution For Class 8 Maths Chapter 6 Image 75

∴ √256 = 16

(iv)

NCERT Solution For Class 8 Maths Chapter 6 Image 76

NCERT Solution For Class 8 Maths Chapter 6 Image 77

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 perfect square.

New number = 1825 + 24 = 1849

NCERT Solution For Class 8 Maths Chapter 6 Image 78

∴ √1849 = 43

(v)

NCERT Solution For Class 8 Maths Chapter 6 Image 79

NCERT Solution For Class 8 Maths Chapter 6 Image 80

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 perfect square.

New number = 6412 + 149 = 656

NCERT Solution For Class 8 Maths Chapter 6 Image 81

∴ √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, area of the field = 441 m2

⇒ a2 = 441 m2

⇒a = √441 m

NCERT Solution For Class 8 Maths Chapter 6 Image 82

∴ 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.

NCERT Solution For Class 8 Maths Chapter 6 Image 83

Given, AB = 6 cm, BC = 8 cm

Let AC be x cm.

∴ AC2 = AB2 + BC2

NCERT Solution For Class 8 Maths Chapter 6 Image 84

Hence, AC = 10 cm.

b.

NCERT Solution For Class 8 Maths Chapter 6 Image 85

Given, AC = 13 cm, BC = 5 cm

Let AB be x cm.

∴ AC2 = AB2 + BC2

⇒ AC2 – BC2 = AB2

NCERT Solution For Class 8 Maths Chapter 6 Image 86

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

Solution:

Let the number of rows and column be, x.

∴ Total number of row and column= x× x = x2 As per question, x2 = 1000

⇒ x = √1000

NCERT Solution For Class 8 Maths Chapter 6 Image 87

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 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 and column be, x.

∴ Total number of row and column= x × x = x2 As per question, x2 = 500

x = √500

NCERT Solution For Class 8 Maths Chapter 6 Image 88

Hence, 16 children would be left out in 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 square root by division method
  2. Square Roots of Decimals
  3. Estimating Square Root

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