*MATHS*
CLASS - 8
CHAPTER 6
SQUARE AND SQUARE ROOTS
Q5. For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so
obtained:
i) 252
iii) 1008
v) 1458
Q6:For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained:
i) 2925
ii) 2645
iv) 1620
Q1: Find the square root of each of the following numbers by Division method:
i) 2304
ii) 3481
vi) 5776
viii) 1024
PLEASE GIVE CORRECT ANSWERS AND ACCORDING TO THE GIVEN METHOD GIVEN IN THE QUESTION . I WILL MARK BRAINLIEST.
Answers
Answer:
answer is 7 for question no 1. 1
Q.5 Solution:
i.
NCERT Solution For Class 8 Maths Chapter 6 Image 10
252 = 2×2×3×3×7
= (2×2)×(3×3)×7
Here, 7 cannot be paired.
∴ We will multiply 252 by 7 to get perfect square.
New number = 252 × 7 = 1764
NCERT Solution For Class 8 Maths Chapter 6 Image 11
1764 = 2×2×3×3×7×7
⇒ 1764 = (2×2)×(3×3)×(7×7)
⇒ 1764 = 22×32×72
⇒ 1764 = (2×3×7)2
⇒ √1764 = 2×3×7 = 42
ii.
NCERT Solution For Class 8 Maths Chapter 6 Image 12
180 = 2×2×3×3×5
= (2×2)×(3×3)×5
Here, 5 cannot be paired.
∴ We will multiply 180 by 5 to get perfect square.
New number = 180 × 5 = 900
NCERT Solution For Class 8 Maths Chapter 6 Image 13
900 = 2×2×3×3×5×5×1
⇒ 900 = (2×2)×(3×3)×(5×5)
⇒ 900 = 22×32×52
⇒ 900 = (2×3×5)2
⇒ √900 = 2×3×5 = 30
iii.
NCERT Solution For Class 8 Maths Chapter 6 Image 14
1008 = 2×2×2×2×3×3×7
= (2×2)×(2×2)×(3×3)×7
Here, 7 cannot be paired.
∴ We will multiply 1008 by 7 to get perfect square.
New number = 1008×7 = 7056
NCERT Solution For Class 8 Maths Chapter 6 Image 15
7056 = 2×2×2×2×3×3×7×7
⇒ 7056 = (2×2)×(2×2)×(3×3)×(7×7)
⇒ 7056 = 22×22×32×72
⇒ 7056 = (2×2×3×7)2
⇒ √7056 = 2×2×3×7 = 84
iv.
NCERT Solution For Class 8 Maths Chapter 6 Image 16
2028 = 2×2×3×13×13
= (2×2)×(13×13)×3
Here, 3 cannot be paired.
∴ We will multiply 2028 by 3 to get perfect square. New number = 2028×3 = 6084
NCERT Solution For Class 8 Maths Chapter 6 Image 17
6084 = 2×2×3×3×13×13
⇒ 6084 = (2×2)×(3×3)×(13×13)
⇒ 6084 = 22×32×132
⇒ 6084 = (2×3×13)2
⇒ √6084 = 2×3×13 = 78
v.
NCERT Solution For Class 8 Maths Chapter 6 Image 18
1458 = 2×3×3×3×3×3×3
= (3×3)×(3×3)×(3×3)×2
Here, 2 cannot be paired.
∴ We will multiply 1458 by 2 to get perfect square. New number = 1458 × 2 = 2916
NCERT Solution For Class 8 Maths Chapter 6 Image 19
2916 = 2×2×3×3×3×3×3×3
⇒ 2916 = (3×3)×(3×3)×(3×3)×(2×2)
⇒ 2916 = 32×32×32×22
⇒ 2916 = (3×3×3×2)2
⇒ √2916 = 3×3×3×2 = 54
vi.
NCERT Solution For Class 8 Maths Chapter 6 Image 20
768 = 2×2×2×2×2×2×2×2×3
= (2×2)×(2×2)×(2×2)×(2×2)×3
Here, 3 cannot be paired.
∴ We will multiply 768 by 3 to get perfect square.
New number = 768×3 = 2304
NCERT Solution For Class 8 Maths Chapter 6 Image 21
2304 = 2×2×2×2×2×2×2×2×3×3
⇒ 2304 = (2×2)×(2×2)×(2×2)×(2×2)×(3×3)
⇒ 2304 = 22×22×22×22×32
⇒ 2304 = (2×2×2×2×3)2
⇒ √2304 = 2×2×2×2×3 = 48