How do you simplify (square root 2) + 2 (square root 2) + (square root 8) / (square root 3)?

1 Answer
Sep 6, 2015

Answer:

#5/3 * sqrt(6)#

Explanation:

I'll assume that the expression looks like this

#(sqrt(2) + 2sqrt(2) + sqrt(8))/sqrt(3)#

Start by focusing on the numerator. More specifically, notice that you can rewrite #sqrt(8)# as

#sqrt(8) = sqrt(4 * 2) = sqrt(4) * sqrt(2) = 2 * sqrt(2)#

The numerator will then take the form

#sqrt(2) + 2 sqrt(2) + 2sqrt(2) = 5sqrt(2)#

Next, you need to rationalize the denominator. To do that, multiply the fraction by #1 = sqrt(3)/sqrt(3)#

#(5sqrt(2))/sqrt(3) * sqrt(3)/sqrt(3) = (5 * sqrt(2) * sqrt(3))/(sqrt(3) * sqrt(3)) = (5 * sqrt(2 * 3))/sqrt(3 * 3)#

The final form of the expression will be

#(5 * sqrt(6))/sqrt(3^2) = color(green)(5/3 * sqrt(6))#