**Cube root **of a number can be found by a very simple method which is the prime factorization method. Finding the cubic root of non-perfect cube number is a little complex process but can be mastered easily. To find the cube root of any number, we need to find a number which when multiplied three times by itself gives the original number. Example: **∛8** = **∛(2 × 2 × 2) = 2. **Since 8 is a perfect cube number, it is easy to find the cube root of a number.

Let us consider another example of number 2. Since 2 is not a **perfect cube** number. It is not easy to find the cubic root of 2. With the help of the long division method, it is possible to find the cube roots for non-perfect cube numbers. The approximate value of the **∛2 is 1.260.**

Cube root is the inverse process of calculating the cube of a number. It is denoted by the symbol ‘**∛’**. Let us see some examples here now.

To find the cube root of a number 64, we want a number which when multiplied thrice with itself shall give 64. We can write,

64 = 4 × 4× 4 = 4^{3}

Taking cubic root on both the sides;

or **∛**64 = **∛**4^{3}

Therefore, cube-root of 64 is 4.

Please note that we will only consider the positive values cube roots of the natural numbers.

Number | Cube(a^{3}) |
Cube root ∛a |
---|---|---|

1 | 1 | 1.000 |

2 | 8 | 1.260 |

3 | 27 | 1.442 |

4 | 64 | 1.587 |

5 | 125 | 1.710 |

6 | 216 | 1.817 |

7 | 343 | 1.913 |

8 | 512 | 2.000 |

9 | 729 | 2.080 |

10 | 1000 | 2.154 |

11 | 1331 | 2.224 |

12 | 1728 | 2.289 |

13 | 2197 | 2.351 |

14 | 2744 | 2.410 |

15 | 3375 | 2.466 |

We can find the cube-root of a number by the method of prime factorisation. Consider the following example for a clear understanding:

2744= 2 × 2× 2 × 7 ×7 × 7= (2 × 7 )^{3}

Therefore, the cube root of 2744 = ∛2744 = 2 × 7 = 14

Let us find the cube root of 343 with the help of the prime factorization method.

Dividing 343 by smallest prime factor, till we get the remainder as 1. Follow the below steps;

Cube root of 343

Therefore, 343 = 7 × 7 × 7

And, **∛343 = 7**

Now, let’s find the cubic root of 729.

Cube root of 729

729 = 3 × 3 × 3 × 3 × 3 × 3 = 9 × 9 × 9

Therefore, the cube root of 729 i.e. **∛729 = 9**

**Question 1:** Solve: ∛24389

**Solution:**

Prime factors = 29×29×29 = 293

Therefore ∛24389= 29.

**Question 2:** Find ∛46656 by the method of prime factorization.

**Solution:**

Let us first find the prime factors:

Cube Root of Numbers

∛46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 = 23 × 2^{3} × 3^{3} × 3^{3} = (2 × 2 × 3 × 3)^{3}

Therefore, ∛46656= 36.

The cube root of a number is defined as the number which results in the original number when cubed. For example, for 8, the cube root will be 2 as 2×2×2 = 8.

The cube root of perfect cubes can be easily found out by using prime factorization method as explained in this lesson.

A perfect cube is defined as any number which is the cube of an integer.

To check whether a number is a perfect cube, factorize the number first. If the factors of the number can be equally grouped in triples, the number is a perfect cube.