Question
Find the square root of the following by prime factorization.$7056$
✓
Answer
Resolving 7056 into prime factors, $7056 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7 \times 7$
$\begin{array}{c|c}2& 7056 \\ \hline 2 & 3528 \\\hline 2&1764 \\\hline2&882\\\hline3&441\\\hline3&147\\\hline7&49\\\hline7&7\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $7056 = (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times (7 \times 7)$
Taking one factor for each pair, we get the square root of $705 2 \times 2 \times 3 \times 7 = 84$
$\begin{array}{c|c}2& 7056 \\ \hline 2 & 3528 \\\hline 2&1764 \\\hline2&882\\\hline3&441\\\hline3&147\\\hline7&49\\\hline7&7\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $7056 = (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times (7 \times 7)$
Taking one factor for each pair, we get the square root of $705 2 \times 2 \times 3 \times 7 = 84$
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