FreeAlgebra Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Cube Root

## Definition of Cube Root

To indicate a cube root, we use the same radical symbol we used for square roots, but we write a small 3 just above the on the radical symbol to indicate a cube root. The small 3 is called the index of the radical.

For example, the cube root of 64 is written

Definition â€” Cube Root

The cube root of a real number, a, is written If b is a real number and b3 = a, then

Example: because 43 = 64.

Here are some examples:

because 53 = 5 Â· 5 Â· 5 = 125

because 13 = 1 Â· 1 Â· 1 = 1.

= 1 because (-1)3 = (-1)(-1)(-1) = -1.

because (-2)3 = (-2)(-2)(-2) = -8.

Note:

To find the cube root of a number, we reverse the operation of cubing.

For example, to find we ask â€œWhat number cubed is 8?â€.

Therefore,

The last two examples show that a cube root, unlike a square root, can have a negative radicand.

We can use geometry to provide a visual interpretation of a cube root.

For example, suppose a cube has a volume of 125 cubic inches. The length of each side is the cube root of the volume.

That is, the length of a side of the cube == 5 in.

A perfect cube is a number that has a rational cube root.

For example, 125 is a perfect cube because 53 = 125.

As we work with cube roots, we will find it useful to recognize perfect cubes and their cube roots.

Now we will summarize the relationship between cubes and cube roots.

Property â€” Cubes and Cube Roots

English Cubing and taking a cube root â€œundoâ€ each other.

Algebra If a is a real number, then

Example

Note:

Unlike square roots, there are no â€œprincipalâ€ cube roots.

The sign of a cube root depends on the sign of its radicand.

 Perfect Squares Principal Square Roots 03 = 0 13 = 1 23 = 4 33 = 9 43 = 16 53 = 25 63 = 36 73 = 49 83 = 64 93 = 81 103 = 100

Property â€” Cubes and Cube Roots

English Cubing and taking a cube root â€œundoâ€ each other.

Algebra If a is a real number, then

Example