Find the square root of the following by prime factorization.1166… - Vidyadip

Question

Find the square root of the following by prime factorization.$11664$

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Answer

Resolving 11664 into prime factors,$11664 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$
$\begin{array}{c|c}2& 11644 \\ \hline 2 & 5832 \\\hline 2&2916 \\\hline2&1458 \\\hline3&729\\\hline3&243\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
$11664 = (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times (3 \times 3) \times (3 \times 3)$
Taking one factor for each pair, we get the square root of $11664$
$2 \times 2 \times 3 \times 3 \times 3 = 108$

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