Question

Find the least number by which 1800 should be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square thus obtained

Answer 1

We find 1800 = 2 × 2 × 3 × 3 × 5 × 5 × 2

= 2² × 3² × 5² × 2

Here the last factor 2 has no pair.

So if we multiply 1800 by 2, then the number becomes a perfect square.

2	1800
2	900
3	450
3	150
5	50
5	10
2	2
	1

∴ 1800 × 2 = 3600 is the required perfect square number.

∴ 3600 = 1800 × 2

3600 = 2² × 3² × 5² × 2 × 2

3600 = 2² × 3² × 5² × 2²

= (2 × 3 × 5 × 2)² 

`sqrt(3600) = sqrt((2 xx 3 xx 5 xx 2)^2`

= 2 × 3 × 5 × 2

= 60

∴ `sqrt(3600)` = 60