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treypence05 · Jan 25, 2012, 05:57 PM

I'm having trouble simplifying this. ^3 to the square root of negative 27

Aurora2000 · Jan 26, 2012, 02:45 AM

Do you mean $\sqrt{-27}^3$ ?

You cannot solve it in the real numbers: $\sqrt{-27}=3\sqrt{3}i$ , and $\sqrt{-27}^3= -81\sqrt{3}i$ , where $i:=\sqrt{-1}$ .

ebaines · Jan 26, 2012, 06:42 AM

I wonder if the OP means this:

$<br /> \sqrt[3] {-27}<br />$

What you're looking for is the cube root of -27, or a number N that satisfies $N \times N \times N = -27$ . Here's a hint: if N is a negative number the result is also negative: for example of N = -2 then $(-2) \times (-2) \times (-2) = -8$ . Perhaps now you can come up with a value for N that works?

Aurora2000 · Jan 26, 2012, 07:06 AM

I think ebaines's guess makes more sense, but it is unusual to write "square root" in this case.