What is the simplified form of (cube root of)16

Question

amistre64 · Answer

simplified form?

anonymous · Answer

Yup! That's what it says!

amistre64 · Answer

what would constitute a simplified form?

anonymous · Answer

A radical??????????? idk

amistre64 · Answer

cbrt(16) IS a radical .... im assuming they might want you to take out the perfect cubes and place them outside of the radical

amistre64 · Answer

that is easiest done by factoring 16 into its prime factors

anonymous · Answer

So.....   16
          /  /
        4  4
     2 2 2 2?????

amistre64 · Answer

thats good :)

now group them in sets of 3 like this:

cbrt[(2.2.2) 2]

and remove the the groups outside of the radical

2 cbrt(2) would appear to be it

amistre64 · Answer

essentially what that does is:

cbrt(2^3) cbrt(2) ; to which the cbrt and the ^3 cancel out

amistre64 · Answer

another method is to convert the radical to an exponent:

16^(1/3) = 2^(3/3) * 2^(1/3) = 2*2^(1/3) = 2 cbrt(2)

anonymous · Answer

2 cbrt(2) doesn't equal 16 though.....

amistre64 · Answer

why would it?

2 cbrt(2) = cbrt(16) ; which is what i believe you initially asked about

anonymous · Answer

OOHHHH! FANTASTIC! Thank you!

amistre64 · Answer

:)  youre welcome