Cube Root

A Cube Root of a number is a number that, when multiplied by itself three times, equals the original number. For example, the cube root of 27 is 3 because `3 × 3 × 3 = 27`

. The symbol for the cube root is `∛`

, so we can write `∛27 = 3`

.

The cube root of a number is the inverse operation of the cube of a number. The cube of a number is the product of the number and itself twice, so for example, the cube of 3 is `3 × 3 × 3 = 27`

.

All real numbers have exactly one real cube root. However, complex numbers can have three distinct complex cube roots.

Here are some examples of cube roots:

- The cube root of 27 is 3.
- The cube root of 64 is 4.
- The cube root of 1 is 1.

Here are some ways to find the cube root of a number:

- Prime factorization: This method involves factoring the number into its prime factorization and then taking the cube root of each prime factor. For example, to find the cube root of 27, we would factor it as
`3 × 3 × 3`

and then take the cube root of each prime factor, which gives us 3. - Long Division: This method is similar to long division for finding the square root of a number. However, instead of dividing by 2, we divide by 3.
- Calculator: Most calculators have a button for finding the cube root of a number.

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