Find the square root of the following by prime factorization.3013… - Vidyadip

Question

Find the square root of the following by prime factorization.$3013696$

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Answer

Resolving $3013696$ into prime factors, $3013696 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 31 \times 31$
$\begin{array}{c|c}2&3013696 \\ \hline 2 & 1506848 \\\hline 2&753424\\\hline2&376712 \\\hline2&188356\\\hline2&941781\\\hline7&47089\\\hline7&6727\\\hline31&961\\\hline31&31\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $3013696 = (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (7 \times 7) \times (31 \times 31)$ Taking one factor for each pair, we get the square root of $3013696 2 \times 2 \times 2 \times 7 \times 31 = 1736$

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