Rationalizing denominator of $\frac{18}{\sqrt{162}}$. Cannot match textbook solution I am given this expression and asked to simplify by rationalizing the denominator:
$$\frac{18}{\sqrt{162}}$$
The solution is provided:
$\sqrt{2}$
I arrived at:
$$\frac{\sqrt{162}}{9}$$
Here is my thought process to arrive at this incorrect answer:
$\frac{18}{\sqrt{162}}$ 
= $\frac{18}{\sqrt{162}}$ * $\frac{\sqrt{162}}{\sqrt{162}}$ 
= $\frac{18\sqrt{162}}{162}$ 
= $\frac{\sqrt{162}}{9}$
How can I arrive at $\sqrt{2}$ ?

$\frac{\sqrt{162}}{9} = \frac{\sqrt{2 \cdot 9^2}}{9} = \frac{9\sqrt{2}}{9} = \sqrt{2}$.
