#### Question

Without doing any calculation, find the number which are surely not perfect squares

(1) 153

(2) 257

(3) 408

(4) 441

#### Solution

The perfect squares of a number can end with any of the digits 0, 1, 4, 5, 6, or 9 at unit’s place. Also, a perfect square will end with even number of zeroes, if any.

1) Since the number 153 has its unit’s place digit as 3, it is not a perfect square.

2) Since the number 257 has its unit’s place digit as 7, it is not a perfect square.

3) Since the number 408 has its unit’s place digit as 8, it is not a perfect square.

4) Since the number 441 has its unit’s place digit as 1, it is a perfect square.

Is there an error in this question or solution?

Solution Without Doing Any Calculation, Find the Number Which Are Surely Not Perfect Squares 153 257 408 441 Concept: Square Roots - Finding Square Roots.