Question

Find the smallest numberby which 1800 must be multipliedso that it comesa perfect spuare also find the square root of a perfect square so obtained

Answer 1

1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5

2180029002450322537552555 1

Grouping the factors into pairs:

1800 = (2 x2 ) x (3 x 3) x (5x 5) x2

Here the factor 2 does not occur in pairs. To be a perfect square, all the factors have to be in pairs. Hence, the smallest number by which 1800 must be divided for it to be a perfect square is 2.