Is my TI-89 lying to me? (simplifying a radical expression)

I have a rather simple radical expression I'm trying to simplify: cube root of (-8*x^6), where x is assumed positive. I think it is simply -2*x^2, but when I entered it into the calculator, I got (x^2) + (square root of 3*x^2***i**). The calculator doesn't seem to be in the habit of lying, and the syntax is entered correctly. Anyone know what I'm missing here? Thanks in advance :)

Re: Is my TI-89 lying to me? (simplifying a radical expression)

A calculator cannot take the regular cube root of a negative number.

To get the right result, make the expression positive first, then take the cube root, and then add the minus sign again.

The "i" you got is the so called *imaginary number*.

It is a correct result, but it takes you out of the world of the real numbers into the so called *complex numbers*.

In particular, the cube root has multiple values when extended to the complex numbers.

Re: Is my TI-89 lying to me? (simplifying a radical expression)

Press MODE on your TI-89, select Complex Format, open the sub menu and see that REAL is selected rather than RECTANGULAR.

Re: Is my TI-89 lying to me? (simplifying a radical expression)

Thanks a ton! I was wondering if it was something of a "limitation" of the calculator that was giving me the complex form, and yeah BobP, I'll try that now with the TI-89. Thanks again guys, VERY good board here :)

Re: Is my TI-89 lying to me? (simplifying a radical expression)

Haha, a "limitation" of the mode I had it set on lol... yeah switching to real yields the "real" answer...