JAMB 1986 · UME · Q4

Find the smallest number by which 252 can be multiplied to obtain a perfect square.

Worked solution (try it first)

Write 252 as a product of primes: $252 = 4 \times 63$
$= 2^2 \times 3^2 \times 7$ .
A perfect square has every prime to an even power.
The 2s and 3s are already paired.
Only the 7 is on its own.
So multiply by 7: $252 \times 7 = 1764 = 42^2$ , option D.