Find the square root of the following by prime factorization. 196 - Vidyadip

Question

Find the square root of the following by prime factorization.
196

✓

Answer

Resolving 196 into prime factors,
196 = 2 × 2 × 7 × 7
$\begin{array}{c|c}2& 196 \\ \hline 2 & 98 \\\hline 7&49 \\\hline 7&7 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
196 = (2 × 2) × (7 × 7)
Taking one factor for each pair, we get the square root of 196
2 × 7 = 14

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