What is a cube root function?

Answer 1

The cube root function is the inverse of the cube function.

So, given a number y, the cube root function seeks to find a number, x, such that multiplying 1 by that number 3 times gives y. [Note that this is equivalent to multiplying the number by itself two times, not three.]

That is, cuberoot(y) = x <=> x^3 = y

For example,

2*2*2 = 8 so the cube root of 8 is 2.

1.5^3 = 3.375 so the cube root of 3.375 is 1.5

(-3)^3 = -27 so the cube root of -27 is -3.

The cube root of y is denoted by y^(1/3). It can also be written using the radical symbol like for a square-root, but the radical must be preceded by a superscript 3. Apologies, but this browser is crap and so I cannot show that representation.

Answer 2

The cube root function may be viewed as the inverse of the cube function.

That is, if x = y^3 then y = cuberoot(x) or x^(1/3).