How do you simplify 2 sqrt(3) *times* (5 sqrt(2) + 5 sqrt(5))2√3⋅×⋅(5√2+5√5)?

1 Answer
LizZ
Sep 3, 2017

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

Explanation:

You cannot add unlike square roots, but you can multiply them. The only thing to do here is to distribute 2sqrt(3)2√3 to the two terms inside the parentheses. So 2sqrt(3)*5sqrt(2)=(2*5)(sqrt(3*2))=10sqrt(6)2√3⋅5√2=(2⋅5)(√3⋅2)=10√6
Likewise, 2sqrt(3)*5sqrt(5)=(2*5)(sqrt(3*5))=10sqrt(15)2√3⋅5√5=(2⋅5)(√3⋅5)=10√15
Add these together, and
2sqrt(3)(5sqrt(2)+5sqrt(5))=10sqrt(6)+10sqrt(15)2√3(5√2+5√5)=10√6+10√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.

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