Q101 of 142 Page 88

By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient.

Given: 216

Factors of 216 = 2 × 2 × 2 × 3 × 3 × 3

As we see, 2 and 3 do not have pair.

Hence 216 should be divided with 2 × 3 to get perfect square.

⇒ 216 should divide with 6.

Now, after division we get 36 = 6²

Now, 36 is a perfect square and 6 is its square root.

Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

100

Write two Pythagorean triplets each having one of the numbers as 5.

102

By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.

103

Find the square root of the following by long division method.

(a) 1369 (b) 5625