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

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify: (sqrt(50) - 2sqrt(5))(5sqrt(2) + sqrt(20))      Log On


   

Question 262842: Simplify:
(sqrt(50) - 2sqrt(5))(5sqrt(2) + sqrt(20))
Found 2 solutions by dabanfield, MathTherapy:
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

Answer by MathTherapy(10702) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:

(sqrt(50) - 2sqrt(5))(5sqrt(2) + sqrt(20))

The many calculations by the other person are TOTALLY UNNECESSARY!! 

%28sqrt%2850%29+-+2sqrt%285%29%29%285sqrt%282%29+%2B+sqrt%2820%29%29
2sqrt%285%29 = sqrt%2820%29
5sqrt%282%29 = sqrt%2850%29

So, %28sqrt%2850%29+-+2sqrt%285%29%29%285sqrt%282%29+%2B+sqrt%2820%29%29 
    %28sqrt%2850%29+-+sqrt%2820%29%29%28sqrt%2850%29+%2B+sqrt%2820%29%29 
    sqrt%2850%29%5E2+-+sqrt%2820%29%5E2 = 50 - 20 = 30