# How do you simplify sqrt(6250)?

Apr 11, 2016

$\sqrt{6250} = 25 \sqrt{10}$

#### Explanation:

First split $6250$ into its prime factors:

$6250 = 2 \times 5 \times 5 \times 5 \times 5 \times 5 = 2 \cdot {5}^{5}$

We can see that the largest square number which is a factor of $6250$ is:

${5}^{4} = {\left({5}^{2}\right)}^{2} = {25}^{2}$

Hence we find:

$\sqrt{6250} = \sqrt{{25}^{2} \cdot 10} = \sqrt{{25}^{2}} \cdot \sqrt{10} = 25 \sqrt{10}$

since $\sqrt{a b} = \sqrt{a} \sqrt{b}$ for any $a , b \ge 0$