How do you simplify #2 sqrt(3) *times* (5 sqrt(2) + 5 sqrt(5))#?

1 Answer
Sep 3, 2017

Answer:

#2sqrt(3)(5sqrt(2)+5sqrt(5))=10sqrt(6)+10sqrt(15)#

Explanation:

You cannot add unlike square roots, but you can multiply them. The only thing to do here is to distribute #2sqrt(3)# to the two terms inside the parentheses. So #2sqrt(3)*5sqrt(2)=(2*5)(sqrt(3*2))=10sqrt(6)#
Likewise, #2sqrt(3)*5sqrt(5)=(2*5)(sqrt(3*5))=10sqrt(15)#
Add these together, and
#2sqrt(3)(5sqrt(2)+5sqrt(5))=10sqrt(6)+10sqrt(15)#
Because neither of the numbers under the radicals in the answer have a perfect square as a multiple, this is the simplest answer you can get.