Question

By what numbers should each of the following be divided to get a perfect square? Also, find the number whose square is the new number. 

 3698

Answer 1

3698 = 2 x 43 x 43 

 

Grouping them into pairs of equal factors:
3698 = 2 x (43 x 43)
The factor, 2 is not paired. For a number to be a perfect square, each prime factor has to be paired. Hence, 3698 must be divided by 2 for it to be a perfect square.
The new number would be (43 x 43).
Hence, the number whose square is the new number is 43.