Question

show that 500 is not a perfect square

Answer 1

First we will find all factors under the square root: 500 has the square factor of 100.

Let's check this width √100*5=√500. As you can see the radicals are not in their simplest form.

Now extract and take out the square root √100 * √5. Root of √100=10 which results into 10√5

All radicals are now simplified. The radicand no longer has any square factors.