# How do you simplify sqrt((2g^3)/(5z))?

Sep 22, 2015

$\frac{\sqrt{10 g z} \cdot g}{5 z}$

#### Explanation:

First, begin by "distributing" the square root sign to the numerator and denominator:
sqrt(2g^3)/(sqrt(5z)
Now simplify the top:
$\frac{\sqrt{2} \sqrt{{g}^{3}}}{\sqrt{5 z}}$ (because $\sqrt{a b} = \sqrt{a} \sqrt{b}$)

$\frac{\sqrt{2} \cdot g \sqrt{g}}{\sqrt{5 z}}$ (for example, $\sqrt{{2}^{3}} = \sqrt{8} = 2 \sqrt{2}$)

Since it isn't proper to have a square root in the denominator, we take it out by multiplying by $\frac{\sqrt{5 z}}{\sqrt{5 z}}$.

$\frac{\sqrt{2} \cdot g \sqrt{g}}{\sqrt{5 z}} \cdot \frac{\sqrt{5 z}}{\sqrt{5 z}}$

$\frac{\sqrt{2} \cdot g \sqrt{g} \cdot \sqrt{5 z}}{5 z}$ ($\sqrt{5 z} \cdot \sqrt{5 z} = 5 z$)

We can now finally collect all of our radicals (square roots) into one neat sign:

$\frac{\sqrt{10 z g} \cdot g}{5 z}$ (remember that $\sqrt{a} \sqrt{b} \sqrt{c} = \sqrt{a b c}$)

And that is the final answer.