Question
Find the square root of the following by prime factorization. $196$
✓
Answer
Resolving 196 into prime factors, $196 = 2 \times 2 \times 7 \times 7 $
$\begin{array}{c|c}2& 196 \\ \hline 2 & 98 \\\hline 7&49 \\\hline 7&7 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $196 = (2 \times 2) \times (7 \times 7$)
Taking one factor for each pair, we get the square root of $196 2 \times 7 = 14$
$\begin{array}{c|c}2& 196 \\ \hline 2 & 98 \\\hline 7&49 \\\hline 7&7 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $196 = (2 \times 2) \times (7 \times 7$)
Taking one factor for each pair, we get the square root of $196 2 \times 7 = 14$
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