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

Question

Using prime factorization method, find the following numbers are perfect squares? $3549$

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Answer

$3549 = 3 \times 7 \times 13 \times 13$
$\begin{array}{c|c} 3& 3549 \\ \hline 7 & 1183 \\\hline 13&169 \\\hline 13&13 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors, $3549 = (13 \times 13) \times 3 \times 7$ The last factors, $3$ and $7$ cannot be paired.
Hence, $3549$ is not a perfect square.
Hence, the perfect squares are $225, 441, 2916$ and $11025$.

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