Question

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

Answer 1

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 `1/sqrt2` by 16 to get `16/sqrt32`. I would multiply `3/sqrt8` by 4 to get `12/sqrt32`. This leaves you with `16/sqrt32 + 12/sqrt32 + 6/sqrt32`. From here we can add these to get `34/sqrt32`. We can simplify this even more by dividing by two to get `17/sqrt16` this is as simplified as this equation gets.

Answer 2

`2sqrt2`

Explanation:

First we need a common denominator. In this case, we'll use `sqrt32`.

Convert `1/sqrt2` by multiplying it by `sqrt16/sqrt16`

`1/sqrt2 * sqrt16/sqrt16 = sqrt16/sqrt32`

We must also convert `3/sqrt8` by multiplying it by ##

`3/sqrt8 * sqrt4/sqrt4 = (3sqrt4)/sqrt32`

This leaves us with a simple equation:

`sqrt16/sqrt32 + (3sqrt4)/sqrt32 + 6/sqrt32`

Now we simplify the numerators, and finish the equation.

`4/sqrt32 + 6/sqrt32 + 6/sqrt32 = 16/sqrt32`

We can also simplify this.

`16/sqrt32 = 16/(4sqrt2) = 4/sqrt2`

If necessary, this can be rationalized.

`4/sqrt2 * sqrt2/sqrt2 = (4sqrt2)/2 = 2sqrt2`