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

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Answer 1 · 2017-12-05T17:22:16

See below.

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.

Answer 2 · 2017-12-05T18:37:05

#-6#

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#