When we talk about numbers, a root of a number is another number that produces a whole number when it is raised to a certain power (also called an exponent).
Using the number 64 as an example we can see that the 3rd root of the number is 4:
The third root is also commonly known as the cube root and it is very commonly used for solving cubic equations - in particular, to solve the dimensions of a three dimensional object with a certain volume.
It's likely that you have seen or heard of the square root of a number before and the symbol that accompanies it, which is called the radical symbol: √. Any number that is shown alongside this symbol are called radical terms, or radicals for short.
The cube root symbol is very similar to the square root symbol, but has a little 3, which is called the index, shown above the radical symbol. Using the cube root of 64 as an example, it would be shown like so:
Unlike the square root, the result of a cube root calculation can be any real number. That includes, positive numbers, negative numbers, or zero. Also different is that the radicand (in the above example this is the number 64) can also be negative and still achieve 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
When the cube root of a given number is a whole number, this is called a perfect cube. Perfect cubes are important for many mathematical functions and are used in everything from carpentry through to more advanced topics like physics and astronomy.
If we look at the number 64, we know that the cube root is 4, and since this is a whole number, we can say that 64 is a perfect cube.
If you want to learn more about perfect cube numbers we have a list of perfect cubes which covers the first 1,000 perfect cube numbers.
Practice Cube Roots Using Examples
If you want to continue learning about cube roots, take a look at the random calculations in the sidebar to the right of this blog post.
We have listed a selection of completely random numbers that you can click through and follow the information on calculating the cube root of that number to help you understand number roots.