Question

Find the smallest natural number by which 720 should be multiplied to make it a perfect square.

Answer 1

We have to find the smallest number by which 720 should be multiplied to get a perfect square.

Here 720 = 2 x 2 x 2 x 2 x 3 x 3 x 5

We have pairs of 2 and 3 but there is only one 5

Now if we multiply 720 by 5 then we get three complete pairs hence the resultant number will be perfect square.

Hence 720 x 5 = (2 x 2) x (2 x 2) x (3 x 3) x (5 x 5)

∵ \(\sqrt{720\times5}\) = 2 x 2 x 3 x 5 = 60