Question
Find the square root of the following by prime factorization.$586756$
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Answer
Resolving 586756 into prime factors, $586756 = 2 \times 2 \times 383 \times 383$
$\begin{array}{c|c}2&586756 \\ \hline 2 & 293378 \\\hline 383&146689 \\\hline383&383 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $586756 = (2 \times 2) \times (383 \times 383)$ Taking one factor for each pair, we get the square root of $586756 2 \times 383 = 766$
$\begin{array}{c|c}2&586756 \\ \hline 2 & 293378 \\\hline 383&146689 \\\hline383&383 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $586756 = (2 \times 2) \times (383 \times 383)$ Taking one factor for each pair, we get the square root of $586756 2 \times 383 = 766$
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