Find the smallest number by which $396$ must be divided so as to get a perfect square.

Question

$\begin{array}{1 1} 11 \\ 12 \\ 13 \\ 14 \end{array} $

Answer 1

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

Answer 2

The smallest number is 11 as...

Through prime factorisation.

396=2×2×3×3×11

=> 396=(2^2)×(3^2)×11

If we multiply with 11

The equation would turn into

2^2×3^2×11^11

Hence, smallest number must be 11