How do you add square root of 2 plus the square root of 6?

1 Answer
Oct 8, 2015

Answer:

#sqrt(2) * (1 + sqrt(3))#

Explanation:

Your starting expression looks like this

#sqrt(2) + sqrt(6)#

Now, because the square root terms are different, you can't really add these two radicals. However, you could simplify this expression a bit.

Notice that you can write #6# as

#6 = 2 * 3#

This means that you have

#sqrt(2) + sqrt(2 * 3) = sqrt(2) + sqrt(2) * sqrt(3)#

Now use #sqrt(2)# as a common factor to get

#sqrt(2) + sqrt(2) * sqrt(3) = color(green)(sqrt(2) * (1 + sqrt(3))#