Question
Using prime factorization method, find the following numbers are perfect squares?
11025
11025
✓
Answer
11025 = 3 × 3 × 5 × 5 × 7 × 7
$\begin{array}{c|c} 3& 11025 \\ \hline 3 & 3675 \\\hline 5&1225 \\\hline 5&245 \\\hline 7&49 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
11025 = (3 × 2) × (5 × 5) × (7 × 7)
There are no left out of pairs. Hence, 11025 is a perfect square.
$\begin{array}{c|c} 3& 11025 \\ \hline 3 & 3675 \\\hline 5&1225 \\\hline 5&245 \\\hline 7&49 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
11025 = (3 × 2) × (5 × 5) × (7 × 7)
There are no left out of pairs. Hence, 11025 is a perfect square.
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