SOLUTION: (3 sqrt 2) * (-4 sqrt 10)

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Question 200781: (3 sqrt 2) * (-4 sqrt 10)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2Asqrt%282%29%29%2A%28-4%2Asqrt%2810%29%29 Start with the given expression.


%283%29%28-4%29%2A%28sqrt%282%29%2Asqrt%2810%29%29 Rearrange the terms.


-12%2A%28sqrt%282%29%2Asqrt%2810%29%29 Multiply 3 and -4 to get -12


-12%2Asqrt%282%2A10%29 Combine the roots using the identity sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29


-12%2Asqrt%2820%29 Multiply 2 and 10 to get 20


-12%2Asqrt%284%2A5%29 Factor 20 to get 4*5. Note: one of the factors must be a perfect square.


-12%2Asqrt%284%29%2Asqrt%285%29 Break up the roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29


-12%2A2%2Asqrt%285%29 Take the square root of 4 to get 2.


-24%2Asqrt%285%29 Multiply -12 and 2 to get -24


So %283%2Asqrt%282%29%29%2A%28-4%2Asqrt%2810%29%29=-24%2Asqrt%285%29