# What is the perfect square of root 500?

Jun 22, 2018

$= 10 \sqrt{5}$

#### Explanation:

There is not a "perfect square" of $\sqrt{500}$, here is why:

$= \sqrt{500}$ has the prime factors:

$= \sqrt{5 \cdot 5 \cdot 5 \cdot 2 \cdot 2}$

$= \sqrt{{5}^{2} \cdot 5 \cdot {2}^{2}}$

$= 5 \cdot 2 \cdot \sqrt{5}$

$= 10 \cdot \sqrt{5}$

Since 5 is not a perfect square it cannot be removed from the radical in an exact form, i.e. $\sqrt{5}$ is an irrational number.