Question

Which of the following numbers are perfect squares?
(i) 121 (ii) 1136 (iii) 256 (iv) 321 (v) 600

Answer 1

Factories the numbers:

(i) 121 = 11 x 11

$\Rightarrow 121={11}^2$

So, 121 is a perfect square

(ii) 1136 = 2 x 2 x 2 x 2 x 71

Since, 71 is a prime number

So, 1136 is not perfect square

(iii) 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

$\Rightarrow 256={16}^2$

So, 256 is a perfect square

(iv) 321 = 3 x 107

Since, 107 is prime number,

It is not a perfect square.

(v) 600 = 2 x 3 x 10 x 10

So, 600 is not perfect square

Hence, 121 and 256 are perfect squares.