Question
Find the square root of the following by prime factorization.$190969$
✓
Answer
Resolving 190969 into prime factors, $190969 = 19 \times 19 \times 23 \times 23$
$\begin{array}{c|c}19&190969 \\ \hline 19 & 10051 \\\hline 23&529 \\\hline23&23 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $190969 = (19 \times 19) \times (23 \times 23)$
Taking one factor for each pair, we get the square root of $190969 19 \times 23 = 437$
$\begin{array}{c|c}19&190969 \\ \hline 19 & 10051 \\\hline 23&529 \\\hline23&23 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $190969 = (19 \times 19) \times (23 \times 23)$
Taking one factor for each pair, we get the square root of $190969 19 \times 23 = 437$
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