SOLUTION: What is the simplified form of the cubed square root of -1?

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Question 622136: What is the simplified form of the cubed square root of -1?
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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What is the simplified form of the cubed square root of -1?
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Do you mean this expression? %28sqrt%28-1%29%29%5E3
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If you are considering just the real numbers, the square root of -1 in undefined. This makes the entire expression undefined.
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When we consider complex numbers, the square root of -1 is defined. You will often see this represented as the letter i. In this case, your expression simplifies to -i. Here's how:
%28sqrt%28-1%29%29%5E3=sqrt%28-1%29%2Asqrt%28-1%29%2Asqrt%28-1%29
%28sqrt%28-1%29%29%5E3=%28-1%29%2Asqrt%28-1%29=-sqrt%28-1%29
%28sqrt%28-1%29%29%5E3=-i
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I wonder if you meant the cube root of -1?
root%283%2C-1%29
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This expression is defined for the real numbers. When we take the cube root of a number, we want the number, which multiplied by itself three times, gives the number under the radical.
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root%283%2C-1%29=-1 because %28-1%29%28-1%29%28-1%29=-1.
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Hope this helps! Feel free to email me if this doesn't make sense yet, or if I misunderstood your problem.
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~Ms.Figgy
math.in.the.vortex@gmail.com