Question
Show that $500$ is not a perfect square.
✓
Answer
Resolving $500$ into prime factors, we have
$\begin{array}{c|c} 2 & 500 \\ \hline 2 & 250\\\hline5&125\\\hline5&25\\\hline5&5 \\\hline&1\end{array}$
$500 = 2 \times 2 \times 5 \times 5 \times 5$
Grouping the factors into pairs of equal factors, we are left with one factor $5$, which cannot be paired.
Hence, $500$ is not a perfect square.
$\begin{array}{c|c} 2 & 500 \\ \hline 2 & 250\\\hline5&125\\\hline5&25\\\hline5&5 \\\hline&1\end{array}$
$500 = 2 \times 2 \times 5 \times 5 \times 5$
Grouping the factors into pairs of equal factors, we are left with one factor $5$, which cannot be paired.
Hence, $500$ is not a perfect square.
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