Question

7.
For each of the following numbers, find the smallest whole number by which it should
multiplied so as to get a perfect square number. Also, find the square root of the squa
number so obtained.
(a)
162
(b) 180
(c)
512
(d)
1200
(e
1620​

Answer 1

Answer:

A) By Prime factorization we get

162=9×9 ×2

It is clear that in order to get a perfect square, one more 2 is required.

So, 2 is the smallest number which must be multiplied to get a perfect square.

The new no. obtained =162×2=324

Therefore, square root of 324=(9×2)=18

B)By Prime factorization we get

180=3×3×2×2×5

It is clear that in order to get a perfect square, one more 5 is required.

So, 5 is the smallest number which must be multiplied to get a perfect square.

The new no. obtained =180×5=900

Therefore, square root of 900=(3×2×5)=30

C)By Prime factorization we get

512=8×8×8

It is clear that in order to get a perfect square, one more 8 is required.

So, 8 is the smallest number which must be multiplied to get a perfect square.

The new no. obtained =512×8=4096

Therefore, square root of 4096=(8×8)=64

D)By Prime factorization we get

1200=10×10×2×2×3

It is clear that in order to get a perfect square one more 3 is required.

So,3 is the smallest number which must be multiplied to get a perfect square.

The new no.obtained =1200×3=3600

Therefore, square root of 3600=(10×2×3)=60

E)By Prime factorization we get

1620=5×2×2×9×9

It is clear that in order to get a perfect square, one more 5 is required.

So, 5 is the smallest number which must be multiplied to get a perfect square.

The new no.obtained =1620×5=8100

Therefore, square root of 8100=(5×2×9)=90

Step-by-step explanation:

Hope it helps........