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Q)

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

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

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A)
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.

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A)
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