SOLUTION: Simplify the square root of -27 multiplied by the square root of -50

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Question 812624: Simplify the square root of -27 multiplied by the square root of -50
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, please try to post your questions under appropriate categories. This problem has nothing to do with conic sections. I have changed the category to a more appropriate one.

sqrt%28-27%29%2Asqrt%28-50%29
With negative radicands in square roots we are working with complex numbers. ("Radicand" is the name for the expression that appears inside a radical.) It is important to recognize the presence of complex numbers because it will dictate the proper procedure.

When working with complex numbers it is important to rewrite the expression in terms of "i" (which is defined as sqrt%28-1%29) before doing anything else:
sqrt%28-1%2A27%29%2Asqrt%28-1%2A50%29
sqrt%28-1%29%2Asqrt%2827%29%2Asqrt%28-1%29%2Asqrt%2850%29
i%2Asqrt%2827%29%2Ai%2Asqrt%2850%29

Now we can simplify the remaining square roots and then multiply or we can do it the other way around. Since I don't feel like multiplying 27 and 50 I choose to simplify first:
i%2Asqrt%289%2A3%29%2Ai%2Asqrt%2825%2A2%29
i%2Asqrt%289%29%2Asqrt%283%29%2Ai%2Asqrt%2825%29%2Asqrt%282%29
i%2A3%2Asqrt%283%29%2Ai%2A5%2Asqrt%282%29
Now we multiply:
15i%5E2%2Asqrt%283%2A2%29
15%28-1%29%2Asqrt%286%29 Since i%5E2+=+-1
-15%2Asqrt%286%29
This is the simplified result.