Question
Find the square root of the following by prime factorization.8281
✓
Answer
Resolving $8281$ into prime factors,$8281 = 7 \times 7 \times 13 \times 13$
$\begin{array}{c|c}7& 8281 \\ \hline 7 & 1183 \\\hline 13&169 \\\hline13&13 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
$8281 = (7 \times 7) \times (13 \times 13)$
Taking one factor for each pair, we get the square root of $705$
$7 \times 13 = 91$
$\begin{array}{c|c}7& 8281 \\ \hline 7 & 1183 \\\hline 13&169 \\\hline13&13 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
$8281 = (7 \times 7) \times (13 \times 13)$
Taking one factor for each pair, we get the square root of $705$
$7 \times 13 = 91$
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