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Exponents

The Cube Root

The cube root is the reverse operation of cubing a number.

Example

2³ = 8,  so 2 is a cube root of 8.

(-2)³ = -8,  so -2 is a cube root of -8.

As you can see, all numbers have a unique cube root.

The cube root of a positive number b is denoted by  or   (See nth root for more on fractional notation) and the cube root of a negative number -b is .

The graph of x³ is shown below. From the graph we can clearly see that each positive number will have a positive cube root, and each negative number will have a negative cube root.

Now try a few on your own.

Exercise

If the cube root of b is an integer, display it in the box provided; otherwise type NI for "not integer".

b

<< Square Root | Exponents Index | n^th Root >>