Simplify 1/sqrt2+3/sqrt8+6/sqrt3212+38+632. 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/sqrt212 by 16 to get 16/sqrt321632. I would multiply 3/sqrt838 by 4 to get 12/sqrt321232. This leaves you with 16/sqrt32 + 12/sqrt32 + 6/sqrt321632+1232+632. From here we can add these to get 34/sqrt323432. We can simplify this even more by dividing by two to get 17/sqrt161716 this is as simplified as this equation gets.

May 1, 2018

2sqrt222

Explanation:

First we need a common denominator. In this case, we'll use sqrt3232.

Convert 1/sqrt212 by multiplying it by sqrt16/sqrt161616

1/sqrt2 * sqrt16/sqrt16 = sqrt16/sqrt32121616=1632

We must also convert 3/sqrt838 by multiplying it by

3/sqrt8 * sqrt4/sqrt4 = (3sqrt4)/sqrt323844=3432

This leaves us with a simple equation:

sqrt16/sqrt32 + (3sqrt4)/sqrt32 + 6/sqrt321632+3432+632

Now we simplify the numerators, and finish the equation.

4/sqrt32 + 6/sqrt32 + 6/sqrt32 = 16/sqrt32432+632+632=1632

We can also simplify this.

16/sqrt32 = 16/(4sqrt2) = 4/sqrt21632=1642=42

If necessary, this can be rationalized.

4/sqrt2 * sqrt2/sqrt2 = (4sqrt2)/2 = 2sqrt24222=422=22