Question
Find the square root of the following by prime factorization.27225
✓
Answer
Resolving 27225 into prime factors,
27225 = 3 × 3 × 5 × 5 × 11 × 11
$\begin{array}{c|c}3&27225 \\ \hline 3 & 9075 \\\hline 5&3025\\\hline5&605 \\\hline11&121\\\hline11&11\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
27225 = (3 × 3) × (5 × 5) × (11 × 11)
Taking one factor for each pair, we get the square root of 27225
3 × 5 × 11 = 165
27225 = 3 × 3 × 5 × 5 × 11 × 11
$\begin{array}{c|c}3&27225 \\ \hline 3 & 9075 \\\hline 5&3025\\\hline5&605 \\\hline11&121\\\hline11&11\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
27225 = (3 × 3) × (5 × 5) × (11 × 11)
Taking one factor for each pair, we get the square root of 27225
3 × 5 × 11 = 165
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