SOLUTION: Simplify: (sqrt(50) - 2sqrt(5))(5sqrt(2) + sqrt(20))

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Question 262842: Simplify:
(sqrt(50) - 2sqrt(5))(5sqrt(2) + sqrt(20))
Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
Expand by multiplying out the terms:
(sqrt(50) - 2sqrt(5))(5sqrt(2) + sqrt(20)) =
sqrt(50)*5*sqrt(2) + sqrt(50)*sqrt(20) - 2*sqrt(5)*5*sqrt(2) - 2*sqrt(5)*sqrt(20) =
5*sqrt(50*2) + sqrt(50*20) - 10*sqrt(5*2) - 2*sqrt(5*20) [Remember sqrt(a)*sqrt(b) = sqrt(a*b)]
The above is then equal to:
5*sqrt(100) + sqrt(1000) - 10*sqrt(10) - 2*sqrt(100) =
5*10 + sqrt(100*10) - 10*sqrt(10) - 2*10 =
50 + sqrt(100)*sqrt(10) - 10*sqrt(10) - 20 =
50 + 10*sqrt(10) - 10 sqrt(10) - 20 = 30