# How do you simplify sqrt(18) without a calculator?

Feb 2, 2015

One way to simplify this number is to look for alternative ways of writing the number that's under the square root sign.

You must extract the square root from $\text{18}$, which isn't a perfect square. However, if you look closely at this number you'll find that

$18 = 9 \cdot 2$

You know that $\text{9}$ is a perfect square, which means that

$18 = {3}^{2} \cdot 2$

Stick this under the square root and you'll get

$\sqrt{18} = \sqrt{{3}^{2} \cdot 2} = \sqrt{{3}^{2}} \cdot \sqrt{2} = 3 \sqrt{2}$