Question

Question 89

Solve the following question:

Show that 500 is not a perfect square.

Answer 1

Resolving 500 into prime factors, we have
$\begin{array}{cc}2& 500\\ 2& 250\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$500=2\times 2\times 5\times 5\times 5$
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.