Simplify 1/sqrt2+3/sqrt8+6/sqrt32. Help, Plz?

May 1, 2018

The way I would answer this is by first simplifying the bottom denominators as you need those to add. To do this I would multiply $\frac{1}{\sqrt{2}}$ by 16 to get $\frac{16}{\sqrt{32}}$. I would multiply $\frac{3}{\sqrt{8}}$ by 4 to get $\frac{12}{\sqrt{32}}$. This leaves you with $\frac{16}{\sqrt{32}} + \frac{12}{\sqrt{32}} + \frac{6}{\sqrt{32}}$. From here we can add these to get $\frac{34}{\sqrt{32}}$. We can simplify this even more by dividing by two to get $\frac{17}{\sqrt{16}}$ this is as simplified as this equation gets.

May 1, 2018

$2 \sqrt{2}$

Explanation:

First we need a common denominator. In this case, we'll use $\sqrt{32}$.

Convert $\frac{1}{\sqrt{2}}$ by multiplying it by $\frac{\sqrt{16}}{\sqrt{16}}$

$\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{16}}{\sqrt{16}} = \frac{\sqrt{16}}{\sqrt{32}}$

We must also convert $\frac{3}{\sqrt{8}}$ by multiplying it by 

$\frac{3}{\sqrt{8}} \cdot \frac{\sqrt{4}}{\sqrt{4}} = \frac{3 \sqrt{4}}{\sqrt{32}}$

This leaves us with a simple equation:

$\frac{\sqrt{16}}{\sqrt{32}} + \frac{3 \sqrt{4}}{\sqrt{32}} + \frac{6}{\sqrt{32}}$

Now we simplify the numerators, and finish the equation.

$\frac{4}{\sqrt{32}} + \frac{6}{\sqrt{32}} + \frac{6}{\sqrt{32}} = \frac{16}{\sqrt{32}}$

We can also simplify this.

$\frac{16}{\sqrt{32}} = \frac{16}{4 \sqrt{2}} = \frac{4}{\sqrt{2}}$

If necessary, this can be rationalized.

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