Using prime factorization method, find the following numbers are … - Vidyadip

Question

Using prime factorization method, find the following numbers are perfect squares? $441$

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Answer

$441 = 3 \times 3 \times 7 \times 7$
$\begin{array}{c|c} 3& 441 \\ \hline 3 & 147 \\\hline 7&49 \\\hline 7&7\\\hline&1 \end{array}$
Grouping them into pairs of equal factors, $441 = 3 \times 3 \times (7 \times 7)$
There are no left out of pairs.
Hence, $441$ is a perfect square.

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