Question

For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.

768

Answer 1

768 can be factorised as follows:

2	768
2	384
2	192
2	96
2	48
2	24
2	12
3	6
	13

768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

Here, prime factor 3 does not have its pair. If 3 gets a pair, then the number will become a perfect square. Therefore, 768 has to be multiplied with 3 to obtain a perfect square.

Therefore, 768 × 3 = 2304 is a perfect square.

768 × 3 = 2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

∴ `sqrt(2304)` = 2 × 2 × 2 × 2 × 3 = 48