How do you simplify #-216^(1/3)#?

2 Answers
Dec 5, 2017

See below.

Explanation:

It is not absolutely clear whether this is supposed to be #root(3)(-216)# or #-root(3)(216)#

For: #root(3)(-216)#

#root(3)(8*27*-1)=2*3root(3)(-1)=6root(3)(-1)#

For: #-root(3)(216)#

#-root(3)(8*27*1)=2*3root(3)(1)=-6root(3)(1)#

Left in this form allows for complex roots.

Dec 5, 2017

#-6#

Explanation:

It is possible to have the cube root of a negative number, but not the square root of a negative number.

#root(3)(-216) = root3 (-6xx-6xx-6#

#=root3 ((-6)^3)#

#=-6#