Cube Root of Numbers Calculator
In this article, we'll explore what cube root means in math and discuss some of the terms you might use when working with cube roots or perfect cubes.
In math you might hear the term "root" used. One of the most common is the square root.
A root is simply a number which produces a whole number when it is raised to a certain power (which means multiplying by itself a specific number of times).
Let's take a look at an example with the number
27. We can see that the 3rd root of 27 is the number 3:
You might have guessed that the third root is also called the cube root. It's most often used to solve cubic equations like calculating the volume of a three dimensional object.
The symbol for a cube root is very similar to the symbol for square root, which is called the radical symbol:
Any number that is placed alongside the symbol are called radical terms, or radicals.
Here is what the cube root symbol looks like:
There is a number above the radical symbol which is called the index, and this index determines how many times you multiply the number by itself.
So, going back to the example of 27, we would show that as a cube root calculation using the below:
With a cube root, the result of the calculation can be any real number - including positive numbers, negative numbers, or even zero. This is different from square roots, where the number cannot be negative or zero.
Another difference with cube roots is that the radicand (the number 27 in the example) can also be a negative number and it will still produce a real result.
Try out the cube root calculator below to calculate cube roots of various numbers and see how it works.
Enter your number in box A below and click "Calculate" to work out the cube root of the given number.
Perfect Cube Numbers
Just like we have with square roots and perfect squares, when the cube root of a number is a whole number, we call it a perfect cube number.
These are important for a lot of different math functions and can be used in simpler settings like carpenty and room design all the way through to more advanced calculations in physics and astronomy.
For our example above using the number 27, we already know that it's a perfect cube because we worked out that the cube root is 3, and this is a whole number.
To find out more about perfect cube numbers, view our list of perfect cubes to see the first 500 of them.
Practice Cube Roots Using Examples
If you made it this far down the page you must be a very dedicated cube root enthusiast!
In the sidebar on the right hand side we have a list of randomly generated cube root calculations for you to explore. Click any of them to be given details on how to calculate it, what the answer is, and whether or not the number is a perfect cube.