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

2 Answers
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 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.

May 1, 2018

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