# Finding Cube Root – Vedic Maths Way

This is an amazing trick which was always appreciated by the audience I have addressed in various workshops. This awe inspiring technique helps you find out the cube root of a 4 or 5 or 6 digits number mentally.

Before going further on the method to find the cube root, please make a note of the following points –

**1) ** Cube of a 2-digit number will have at max 6 digits (99^3 = 970,299). That implies if you are given with a 6 digit number, its cube root will have 2 digits.

**2) ** This trick works only for perfect cubes, it will not work for any arbitrary 6-digit

**3) ** It works only for integers

Now let us start with the trick to find cube root of a 5 or 6 digit number in vedic mathematic way.

Say you have to find the cube root of **54872**. It is known that it’s a perfect cube.

Now divide this number into two parts. The right hand side should always have 3 digits. Remaining digits will come in left hand side. Do it as shown below.

**54 | 872**

You know the answer will have 2 digits. Digit at tens place and digit at units place. We will get the digit at tens place using the left hand side of the original number (54) and digit at units place using right hand side of the number (872)

**Step 1. **

Memorize these tables (very soon you will know why) –

*Table 1: Cube of 1 to 10*

Number |
Cube |

1 |
1 |

2 |
8 |

3 |
27 |

4 |
64 |

5 |
125 |

6 |
216 |

7 |
343 |

8 |
512 |

9 |
729 |

10 |
1000 |

*Table 2: Unit’s digit of Cube Roots*

Cube Ends in |
Cube Root Ends in |

1 |
1 |

2 |
8 |

3 |
7 |

4 |
4 |

5 |
5 |

6 |
6 |

7 |
3 |

8 |
2 |

9 |
9 |

0 |
0 |

**Step 2. **

For left hand side we need to use table 1. We have to see between which 2 numbers in the 2^{nd} column do 54 lies. In this case it lies between 27 and 64. So we will take the cube root of the smaller number i.e. 27 which is 3.

So 3 is the tens digit of the answer.

**Step 3. **

For right hand side we need to use table 2. Since our original number (the perfect cube) ends in 2 (see 5487**2), **its cube root will ends in 8.

Thus the units digit will be 8.

Combining the results we get the answer as 38.

Thus (54872)^1/3 = 38

Try for perfect cubes like 185193, 42875, 1728.

You might also be interested in the trick of finding square root of any number

I hope you liked the simple trick to find the cube root. Leave your comments below –

can i know how to find the cube roots for 8 digit numbers or 9 digit numbers

Good one thanks

Could you please tell the method to find cube root of 2 digit numbers which are not perfect cubes. Please elaborate

Only 27, 64 are two 2-digit perfect cubes. Cube root of 2 digit numbers will all be between 1 and 5. To find exact you need to solve as usual.

Even I hv made a formula…..