Question
Find the square root of the following by prime factorization.7056
✓
Answer
Resolving 7056 into prime factors,
7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7
$\begin{array}{c|c}2& 7056 \\ \hline 2 & 3528 \\\hline 2&1764 \\\hline2&882\\\hline3&441\\\hline3&147\\\hline7&49\\\hline7&7\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
7056 = (2 × 2) × (2 × 2) × (3 × 3) × (7 × 7)
Taking one factor for each pair, we get the square root of 705
2 × 2 × 3 × 7 = 84
7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7
$\begin{array}{c|c}2& 7056 \\ \hline 2 & 3528 \\\hline 2&1764 \\\hline2&882\\\hline3&441\\\hline3&147\\\hline7&49\\\hline7&7\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
7056 = (2 × 2) × (2 × 2) × (3 × 3) × (7 × 7)
Taking one factor for each pair, we get the square root of 705
2 × 2 × 3 × 7 = 84
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