Find the square root of $2304$ by prime factorization method.

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Solution

Find the square root of $2304$ by prime factorization method
The prime factors of $2304$ can be written as
$2304 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3$
Taking Square root on both sides
$\sqrt{2304} = \sqrt{2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3}$
$\Rightarrow$ $\sqrt{2304} = 2 x 2 x 2 x 2 x 3$
$\Rightarrow$ $\sqrt{2304} = 48$
Hence The square root of $2304$ is $48$

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