A cube root is a special value that when we multiply three times gives us the desired number. Thus, a perfect cube is a cube of a whole number. On the other hand, a cube root is when we multiply the lowest number three times to arrive at the number. The cube root of a number is the factor that we multiply by itself three times to get that number. The symbol for cube root is 3 cube root of, end cube root. The cube root of a number is a special value that, when used in a multiplication three times, gives that number. Example: 3 × 3 × 3 = 27, so the cube root of 27 is 3.
A perfect cube is a number that is the cube of an integer. For example, 125 is a perfect cube since 125 = 5 × 5 × 5 = 53, some other examples of perfect cubes are 1, 8, 27, 64, 125, 216, 343, so on. The opposite of cubing a number is finding the cube root. Since 53 = 125, the cube root of 125 is 5. The cube root of a perfect cube is an integer.
Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They can be expressed as the sum of two cubes in two different ways.