Question
Find the square root of the following by prime factorization.47089
✓
Answer
Resolving 47089 into prime factors,
47089 = 7 × 7 × 31 × 31
$\begin{array}{c|c}7& 47089 \\ \hline 7 & 6727 \\\hline 31&961 \\\hline31&31 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
47089 = (7 × 7) × (31 × 31)
Taking one factor for each pair, we get the square root of 47089
7 × 31 = 217
47089 = 7 × 7 × 31 × 31
$\begin{array}{c|c}7& 47089 \\ \hline 7 & 6727 \\\hline 31&961 \\\hline31&31 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
47089 = (7 × 7) × (31 × 31)
Taking one factor for each pair, we get the square root of 47089
7 × 31 = 217
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