Question
Using prime factorization method, find the following numbers are perfect squares? $189$
✓
Answer
$189 = 3 \times 3 \times 3 \times 7$
$\begin{array}{c|c} 3& 189 \\ \hline 3 & 63 \\\hline 3&21 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors, $189 = (3 \times 3) \times 3 \times 7$
The factors $3$ and $7$ cannot be paired.
Hence, $189$ is not a perfect square.
$\begin{array}{c|c} 3& 189 \\ \hline 3 & 63 \\\hline 3&21 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors, $189 = (3 \times 3) \times 3 \times 7$
The factors $3$ and $7$ cannot be paired.
Hence, $189$ is not a perfect square.
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