SOLUTION: how do you simplify 5√(-6)*4√(-10)

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Question 186676: how do you simplify 5√(-6)*4√(-10)
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%2Asqrt%28-6%29%2A4%2Asqrt%28-10%29 Start with the given expression.


5%2Asqrt%28-1%2A6%29%2A4%2Asqrt%28-1%2A10%29 Factor -6 into -1*6. Factor -10 into -1*10


5%2Asqrt%28-1%29%2Asqrt%286%29%2A4%2Asqrt%28-1%29%2Asqrt%2810%29 Break up the square root.


5%2Ai%2Asqrt%286%29%2A4%2Ai%2Asqrt%2810%29 Replace the square root of -1 with 'i' (note: i=sqrt%28-1%29)


%285%2A4%29%2A%28sqrt%286%29%2Asqrt%2810%29%29%2A%28i%2Ai%29 Rearrange the terms.


%285%2A4%29%2A%28sqrt%286%29%2Asqrt%2810%29%29%2A%28i%5E2%29 Multiply 'i' and 'i' to get i%5E2


%285%2A4%29%2A%28sqrt%286%29%2Asqrt%2810%29%29%2A%28-1%29 Replace i%5E2 with -1. Remember, since i=sqrt%28-1%29, then i%5E2=-1


%285%2A4%2A%28-1%29%29%2A%28sqrt%286%29%2Asqrt%2810%29%29 Rearrange the terms again


-20%2A%28sqrt%286%29%2Asqrt%2810%29%29 Multiply


-20%2Asqrt%286%2A10%29 Combine the roots.


-20%2Asqrt%2860%29%29 Multiply


-20%2Asqrt%284%2A15%29 Factor 60 into 4*15. Note: one factor is a perfect square


-20%2Asqrt%284%29%2Asqrt%2815%29 Break up the square root.


-20%2A2%2Asqrt%2815%29 Take the square root of 4 to get 2


-40%2Asqrt%2815%29 Multiply


So 5%2Asqrt%28-6%29%2A4%2Asqrt%28-10%29=-40%2Asqrt%2815%29

Answer by Alan3354(69443) About Me  (Show Source):