Find the square root of the following by prime factorization.5867… - Vidyadip

Question

Find the square root of the following by prime factorization.586756

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Answer

Resolving 586756 into prime factors,
586756 = 2 × 2 × 383 × 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 × 2) × (383 × 383)
Taking one factor for each pair, we get the square root of 586756
2 × 383 = 766

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