Important Questions For Class 8 Maths- Chapter 6- Squares and Square Roots

Squares and Square Roots is one of the crucial topics of Maths. It is an important topic which also helps in preparing for Board exams for class 10(CBSE). Apart from studying and practicing problems on squares from NCERT, students shall also practice these important questions.

Solving these important questions of class 8 maths chapter 6 will help you prepare for CBSE board exams too.

1.Find a Pythagorean triplet where one number is 16.

Solution: As we know that 2m, m2 – 1, m2 + 1 is considered as a Pythagorean triplet.

As it is given here 2m = 16, so m = 8.

Therefore, m2 – 1 = 64 -1 = 63 and m2 + 1 64 + 1 = 65

16, 63, 65 are the Pythagorean triplet.

2.Show that 121 is the sum of 11 odd natural numbers.

Solution: As 121 = 112

Therefore, 121 = sum of first 11 odd natural numbers

= 1 + 3 + 5+ 7 + 9 + 11 +13 + 15 + 17 + 19 + 21

3. Show that the sum of two consecutive natural numbers is 13 2.

Solution: Here, 2n + 1 = 13

So, n = 6

So, ( 2n + 1)2 = (2n2 + 2n) + (2n2 + 2n + 1)

Substitute n by 6,

(13)2 = ( 2 x 62 + 2 x 6) + (2 x 62 + 2 x 6 + 1)

= 84 + 85

4. Find the squares of the following numbers?

1)25

2) 30

Solution: given a = 25

So a2 = (25)2 = 625

b) here a = 30

a2 = (30)2 = 30 x 30 = 900

5. Use the identity and find the square?

(a =- b) 2 = a2 – 2ab + b2

Solution: 189 = (200 – 11)2 = 40000 – 2 x 200 x 11 + 112 = 40000 – 4400 + 121 = 35721

6. Find the square root of 11025

Solution:

Using prime factorization method: 11025 = 3 x 3 x 5 x 5 x 7 x 7 = (3 x 3) x (5 x 5) x (7 x 7)

√11025 = 3 x 5 x 7 = 105

7. Calculate the value of √99 x √ 396 ?

Solution: √99 x √ 396 = √(99 x 396) = √(3 x 3 x 11 x 2 x 2 x 3 x 3 x 11) = √ (3 x 3 x 3 x 3 x 2 x 2 x 11 x 11) = 3 x 3 x 2 x 11 = 198

8. What would be the square root of 625 using the identity (a +b) 2 = a2 + b2 + 2ab?

Solution: (625)2 = (600 + 25)2 = 6002 + 2 x 600 x 25 +252 = 360000 + 30000 + 625 = 330625

9. Square of even numbers are always ___________?

Solution: Square of even numbers are always even.

10. If two positive numbers a and b are given then,

√ ab = ? and √ (a/b) =

Solution: If two positive numbers a and b are given then,

√ ab = √a x √b and √ (a/b) = √a/√b

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