Our cube root calculator is a handy tool that will help you determine the cube root also called 3rd root of any positive number. Continue reading if you want to learn the cube root definition, familiarize yourself with the properties of the cube root function, and calculate a root of a higher degree. Don't forget to try the square root calculator as well.
Cube root definition
Let's assume you want to find the cube root of number x. The cube root y is such a number that, if raised to third power, will give x as a result. If you formulate this mathematically,
∛(x) = y <=> y^3 = x
A cube root is a special case of exponent. It can be written down as
∛(x) = x ^ (1/3)
Most often, the cube root will not be a rational number (one that can be expressed as a quotient of two natural numbers).
What is the cube root of...?
It is really easy to find the cube root of any positive number with our cube root calculator! Simply type in any number to find its cube root. For example, the cube root of 216 is 6.
Note that it is possible to find a cube root of a negative number as well. After all, a negative number raised to third power is still negative - for instance,
(-6)^3 = -216.
You need to remember, though, that any non-zero number has three cube roots: at least one real one and two imaginary ones. This cube root calculator deals with real numbers only, but we encourage you to read more on the topic of imaginary numbers!
Cube root function
You can graph the function
y = ∛(x). It is an odd function - it means that it is symmetric with respect to the origin and fulfills the condition
- f(x) = f(-x). This function passes through zero.
Most common values
You can find the most common cube root values below. Don't hesitate to use our cube root calculator if the number you want is not on this list!
- ∛(1) = 1
- ∛(8) = 2
- ∛(27) = 3
- ∛(64) = 4
- ∛(125) = 5
- ∛(216) = 6
- ∛(343) = 7
- ∛(512) = 8
- ∛(729) = 9
- ∛(1000) = 10
How to calculate cube root in head?
Do you think that it is possible to solve little problems with cube root without online calculator or even a pencil or paper? If you think that it is impossible or that you are incapable of doing it check this method! It is very easy. Forget all the rules in the arithmetic books and consider for a moment the following method described by Robert Kelly. First of all, it is essential to memorize the cubes of the numbers from 1 to 10 and the last digit of their cubes. It was presented in the table below.
nth root calculator
With our root calculator you can also calculate other roots. Just write the number in the Degree of the root and you will receive any elective nth root calculator! Our calculator will automatically do all necessary calculations and you can freely use it in your calculations! If you want to perform a reverse operation, head to the exponent calculator.