Question 622136
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? {{{(sqrt(-1))^3}}}
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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:
{{{(sqrt(-1))^3=sqrt(-1)*sqrt(-1)*sqrt(-1)}}}
{{{(sqrt(-1))^3=(-1)*sqrt(-1)=-sqrt(-1)}}}
{{{(sqrt(-1))^3=-i}}}

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I wonder if you meant the cube root of -1?
{{{root(3,-1)}}}
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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(3,-1)=-1}}} because {{{(-1)(-1)(-1)=-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