Q99 of 142 Page 88

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

Given: 9720

Factors of 9720 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5

As we see, 3 and 5 do not have a pair to make a cube.

Hence 9720 should be divided with 3 × 3 × 5 to get perfect cube.

⇒ 9720 should divide with 45.

Now, after division we get 216 = 6³

Now, 216 is a perfect cube.

Using prime factorisation, find the cube roots of

(a) 512 (b) 2197

Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

100

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

101

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