Let's explore the cube root of 1. The cube root of a number x is a value y such that when we multiply y by itself three times, we get x. So we need to find what number, when cubed, equals 1.
Now let's test our answer. We need to check if 1 times 1 times 1 equals 1. First, 1 times 1 equals 1. Then, 1 times 1 again equals 1. So 1 cubed equals 1, which confirms our answer.
Let's look at the mathematical notation. The cube root symbol is written as a small 3 above the radical sign. So the cube root of 1 is written as the third root of 1 equals 1. This confirms that 1 raised to the power of 3 equals 1, so the cube root of 1 is indeed 1.
Let's compare the cube root of 1 with other examples. The cube root of 8 is 2, because 2 cubed equals 8. The cube root of 27 is 3, because 3 cubed equals 27. Similarly, the cube root of 1 is 1, because 1 cubed equals 1. Notice the pattern: the cube root operation undoes the cubing operation.
To summarize what we've learned: The cube root of 1 is 1, because 1 times 1 times 1 equals 1. This is written mathematically as the third root of 1 equals 1. Cube roots undo cubing operations, and the number 1 is special because it equals its own cube root.