How do you simplify (5sqrt(8))/ (sqrt(75a))?

May 24, 2015

We first want to get that radical off the bottom. So, we can multiply the numerator and denominator by $\sqrt{75 a}$.

$\frac{\left(5 \sqrt{8}\right) \left(\sqrt{75 a}\right)}{75 a}$

$\frac{5 \sqrt{8 \times 75 a}}{75 a}$

$\frac{5 \sqrt{600 a}}{75 a}$

$\frac{50 \sqrt{6 a}}{75 a}$

$\frac{2 \sqrt{6 a}}{3 a}$