Find the square root of the following by prime factorization.1909… - Vidyadip

Question

Find the square root of the following by prime factorization.190969

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Answer

Resolving 190969 into prime factors,
190969 = 19 × 19 × 23 × 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 × 19) × (23 × 23)
Taking one factor for each pair, we get the square root of 190969
19 × 23 = 437

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