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