The cube root of $27$ is $3$.

To clarify this concept, let’s first define what a cube root is. A cube root of a number is a value that, when multiplied by itself three times (or cubed), results in the original number. Mathematically, if $x$ represents the cube root of $y$, then it follows that:

In the case of the number $27$, we are looking for a number that, when cubed, equals $27$. We can examine the number $3$:

Since this equation holds true, we can confidently conclude that the cube root of $27$ is indeed $3$.

Another perspective to consider is prime factorization. The number $27$ can be expressed as the product of its prime factors:

This representation indicates that $27$ is composed of three factors of $3$ multiplied together. Consequently, the cube root of $27$ corresponds to the number that appears three times in this factorization, which is $3$.

Understanding cube roots is essential in various fields of mathematics, including solving equations and analyzing geometric shapes. For instance, if you know the volume of a cube and need to determine the length of one side, you would calculate the cube root. In this example, if a cube has a volume of $27$ cubic units, then the length of each side of the cube would be $3$ units.