Cube Root

To find cube root, make triple of equal factors. The opposite of cubing a number is called finding the cube root. A cube root is a number, that is multiplied by itself three times in order to create a cubic value. A cube root of a number x is a number, such that a³= x. All real numbers (except zero) have exactly one real cube root.

Cube of 6 = 6³ =216

Cube root of 216 = 6

Examples

• The cube root of 64 is 4 ( because 4x4x4=64)
• The cube root of 125 is 5 ( because 5x5x5=125)
• The cube root of 512 is 8 ( because 8x8x8=512 )

The symbol, \(\sqrt [3]{}\), means cube root, so \(\sqrt [3]{27}\) means "cube root of 27" and \(\sqrt[3]{64}\)means "Cube root of 64"

Thus \(\sqrt [3]{27}\) = \(\sqrt [3]{3^3}\) = 3 and \(\sqrt[3]{64}\) = \(\sqrt[3]{4^3}\) = 4

A natural number is known as a perfect cube or a cube number.

Cube root of a perfect cube can be found by factorization method.

• The number should be the factor of the prime number or should be expressed as the factor of the prime number.
• Make triples of the factor and each triple should be equal.
• Take one factor from each triple.
• The product is the cube root of the given number.

Examples

1. Find the cube root of 2×2×2×3×3×3
   = 2 × 3
   = 6
   
   
2. Find the cube root of 729.
   Solution:
   \(\sqrt[3]{729}\)
   = \(\sqrt[3]{3×3×3×3×3×3}\)
   = \(\sqrt[3]{3^3×3^3}\)
   = 3×3
   = 9