Question
Find the square root of the following by prime factorization.1764
✓
Answer
Resolving 1764 into prime factors,
1764 = 2 × 2 × 3 × 3 × 7 × 7
$\begin{array}{c|c}2& 1764 \\ \hline 2 & 882 \\\hline 3&441 \\\hline3&147 \\\hline7&49\\\hline7&7\\\hline&1 \end{array}$
Grouping the factors into pairs of equal factors,
1764 = (2 × 2) × (3 × 3) × (7 × 7)
Taking one factor for each pair, we get the square root of 1764,
2 × 3 × 7 = 42
1764 = 2 × 2 × 3 × 3 × 7 × 7
$\begin{array}{c|c}2& 1764 \\ \hline 2 & 882 \\\hline 3&441 \\\hline3&147 \\\hline7&49\\\hline7&7\\\hline&1 \end{array}$
Grouping the factors into pairs of equal factors,
1764 = (2 × 2) × (3 × 3) × (7 × 7)
Taking one factor for each pair, we get the square root of 1764,
2 × 3 × 7 = 42
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