# How do you rationalize 2/(sqrt(72y))?

May 16, 2015

Let's remember that we use rationalization in order to remove roots from our denominator.

We proceed to do that by multiplying both numerator and denominator of your function by the same value as the root contained in the denominator. That way the proportion will be maintained and the root will be eliminated because

$\sqrt{f \left(x\right)} \sqrt{f \left(x\right)} = f \left(x\right)$

That is because $\sqrt{f} \left(x\right) = f {\left(x\right)}^{\frac{1}{2}}$, then $f {\left(x\right)}^{\frac{1}{2}} f {\left(x\right)}^{\frac{1}{2}} = f {\left(x\right)}^{\frac{1}{2} + \frac{1}{2}} = f {\left(x\right)}^{1} = f \left(x\right)$

$\frac{2}{\sqrt{72 y}} \left(\frac{\sqrt{72 y}}{\sqrt{72 y}}\right) = 2 \frac{\sqrt{72 y}}{72 y} = \frac{\sqrt{72 y}}{36 y}$
$\sqrt{72 y}$ is the same as $\sqrt{2 \cdot 36 y}$. We can take the root of $36$ out, like this: $6 \sqrt{2 y}$
$\frac{6 \sqrt{2 y}}{36 y} = \frac{\sqrt{2 y}}{6 y}$