Solution :
$396 = 2 \times 2 \times 3 \times 3 \times 11$
We observe that 2 and 3 are grouped in pairs and 11 is left unpaired.
If we divide 396 by the factor 11 then ,
$396 \div 11 =\large\frac{2 \times 2 \times 3 \times 3 \times 11}{11}$
$36 =2 \times 2 \times 3 \times 3$
$36$ which is a perfect square.
The required smallest number is 11.
Answer : 11