Q98 of 142 Page 88

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

Given: 176

Factors of 176 = 2 × 2 × 2 × 2 × 11

As we see, 11 do not have a pair.

Hence 176 should be multiply with 11 to get perfect square.

⇒ 176 × 11 = 2 × 2 × 2 × 2 × 11 × 11

⇒ 1936 = 2²× 2²× 11²

⇒ 1936 = 44²

Which is perfect square of 44.

Using prime factorisation, find the square roots of

(a) 11025 (b) 4761

Using prime factorisation, find the cube roots of

(a) 512 (b) 2197

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.