Solution :
$252 = 2\times 2 \times 3 \times 3 \times 7$
We observe that 2 and 3 are grouped in pairs and the 7 is left un paired.
If we multiply $252$ by the factor 7 then
$252 \times 7 = 2 \times 2 \times 3 \times 3 \times7 \times 7$
$1764 = 2 \times \times \times 3 \times 3 \times 7 \times 7$
Which is a perfect square.
$\therefore$ required number is 7
Answer:7