How do you simplify #sqrt2(sqrt6+sqrt10)#?

1 Answer
Jan 24, 2017

Answer:

Radicals can be multiplied together as long as they are all under the same "root" , like square roots, cube roots, or other roots.

Explanation:

I would expand by Distributing:
#sqrt(2)*sqrt(6) + sqrt(2)*sqrt(10)#
= #sqrt(2)sqrt(2)sqrt(3) + sqrt(2)sqrt(2)sqrt(5)#
and look for "pairs" of matching roots.
=#sqrt(2^2)sqrt(3)+sqrt(2^2)sqrt(5)# (you could even skip this step)
= #2sqrt(3) + 2sqrt(5)#.

Pairs of roots that are the same factor simplify easily:
#sqrt(93)sqrt(93) = 93# every time!!