Question

Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number. 

 

Answer 1

The prime factorisation of 3645:
3645 = 3 x 3 x 3 x 3 x 3 x 3 x 5
Grouping the factors into pairs of equal factors, we get:
3645 = (3 x 3) x (3 x 3) x (3 x 3) x 5
The factor, 5 does not have a pair. Therefore, we must divide 3645 by 5 to make a perfect square. The new number is:
(3 x 3) x (3 x 3) x (3 x 3) = 729
Taking one factor from each pair on the LHS, the square root of the new number is 3 x 3 x 3, which is equal to 27.