# How do you simplify the square root of 1/8??

May 26, 2018

$\frac{\sqrt{2}}{4}$

#### Explanation:

$\sqrt{\frac{1}{8}}$

$= \frac{1}{\sqrt{8}}$

$= \frac{1}{2 \sqrt{2}}$

$= \frac{1}{2 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$= \frac{\sqrt{2}}{4}$

May 26, 2018

$\frac{\sqrt{2}}{4}$

#### Explanation:

As per the question, we have

$\sqrt{\frac{1}{8}}$

$= \frac{\sqrt{1}}{\sqrt{8}}$

$= \frac{1}{\sqrt{4 \cdot 2}}$

$= \frac{1}{2 \sqrt{2}}$

Now, we have done half the work, and now we have to rationalize the remaining number to get the most simplified result.

$\therefore \frac{1}{2 \sqrt{2}} \cdot \frac{2 \sqrt{2}}{2 \sqrt{2}}$

$= \frac{2 \sqrt{2}}{2 \sqrt{2}} ^ 2$

$= \frac{2 \sqrt{2}}{4 \cdot 2}$

$= \frac{2 \sqrt{2}}{8}$

$= \frac{\cancel{2} \sqrt{2}}{\cancel{2} \cdot 4}$

$= \frac{\sqrt{2}}{4}$