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

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Answer 1 · 2015-10-08T23:45:30

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

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))#