Find the square root of the following by prime factorization. 441 - Vidyadip

Question

Find the square root of the following by prime factorization.
441

✓

Answer

Resolving 441 into prime factors,
441 = 3 × 3 × 7 × 7
$\begin{array}{c|c}3& 441 \\ \hline 3 & 147 \\\hline 7&49 \\\hline 7&7 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
441 = (3 × 3) × (7 × 7)
Taking one factor for each pair, we get the square root of 441
3 × 7 = 21

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