Question
Find the square root of the following by prime factorization. $441$
✓
Answer
Resolving $441$ into prime factors, $441 = 3 \times 3 \times 7 \times 7$
$\begin{array}{c|c}3& 441 \\ \hline 3 & 147 \\\hline 7&49 \\\hline 7&7 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $441 = (3 \times 3) \times (7 \times 7)$
Taking one factor for each pair, we get the square root of $441 3 \times 7 = 21$
$\begin{array}{c|c}3& 441 \\ \hline 3 & 147 \\\hline 7&49 \\\hline 7&7 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $441 = (3 \times 3) \times (7 \times 7)$
Taking one factor for each pair, we get the square root of $441 3 \times 7 = 21$
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