Find the square root of the following by prime factorization.2433… - Vidyadip

Question

Find the square root of the following by prime factorization.$24336$

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Answer

Resolving 24336 into prime factors, $24336 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 13 \times 13$
$\begin{array}{c|c}2& 24336 \\ \hline 2 & 12168 \\\hline 2&6084 \\\hline2&3042 \\\hline3&1521 \\\hline 3&507\\\hline13&169\\\hline13&13\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $24336 = (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times (13 \times 13)$
Taking one factor for each pair,
we get the square root of $24336 2 \times 2 \times 3 \times 13 = 156$

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