Question:
Show that 500 is not a perfect square.
Solution:
Resolving 500 into prime factors, we have
$500=2 \times 2 \times 5 \times 5 \times 5$
Grouping the factors into pairs of equal factors, we get
$500=(2 \times 2) \times(5 \times 5 \times 5)$
Clearly, by grouping into pairs of equal factors, we are left with one factor 5 , which cannot be paired.
Hence, 500 is not a perfect square.