It may take two-three minutes to find out cube root of a perfect cube by using conventional method. However we can find out cube roots of perfect cubes very fast, say in one-two seconds using Vedic Mathematics.

We need to remember some interesting properties of numbers to do these quick mental calculations which are given below.

1. To calculate cube root of any perfect cube quickly, we need to remember the cubes of 1 to 10 which is given below.

1^{3} | = | 1 |

2^{3} | = | 8 |

3^{3} | = | 27 |

4^{3} | = | 64 |

5^{3} | = | 125 |

6^{3} | = | 216 |

7^{3} | = | 343 |

8^{3} | = | 512 |

9^{3} | = | 729 |

10^{3} | = | 1000 |

2. From the above cubes of 1 to 10, we need to remember an interesting property.

1^{3} = 1 | => | If last digit of the perfect cube = 1, last digit of the cube root = 1 |

2^{3} = 8 | => | If last digit of the perfect cube = 8, last digit of the cube root = 2 |

3^{3} = 27 | => | If last digit of the perfect cube = 7, last digit of the cube root = 3 |

4^{3} = 64 | => | If last digit of the perfect cube = 4, last digit of the cube root = 4 |

5^{3} = 125 | => | If last digit of the perfect cube =5, last digit of the cube root = 5 |

6^{3} = 216 | => | If last digit of the perfect cube = 6, last digit of the cube root = 6 |

7^{3} = 343 | => | If last digit of the perfect cube = 3, last digit of the cube root = 7 |

8^{3} = 512 | => | If last digit of the perfect cube = 2, last digit of the cube root = 8 |

9^{3} = 729 | => | If last digit of the perfect cube = 9, last digit of the cube root = 9 |

10^{3} = 1000 | => | If last digit of the perfect cube = 0, last digit of the cube root = 0 |

It’s very easy to remember the relations given above because

1 | -> | 1 | (Same numbers) |

8 | -> | 2 | (10's complement of 8 is 2 and 8+2 = 10) |

7 | -> | 3 | (10's complement of 7 is 3 and 7+3 = 10) |

4 | -> | 4 | (Same numbers) |

5 | -> | 5 | (Same numbers) |

6 | -> | 6 | (Same numbers) |

3 | -> | 7 | (10's complement of 3 is 7 and 3+7 = 10) |

2 | -> | 8 | (10's complement of 2 is 8 and 2+8 = 10) |

9 | -> | 9 | (Same numbers) |

0 | -> | 0 | (Same numbers) |

Also see

8 -> 2 and 2 -> 8

7 -> 3 and 3-> 7

If we observe the properties of numbers, Mathematics will be a very interesting subject and easy to learn. Now let’s see how we can actually find out the cube roots of perfect cubes very fast.

**Step 1 **

Identify the last three digits and make groups of three three digits from right side. i.e., 4913 can be written as

4, 913

**Step 2**

Take the last group which is 913. The last digit of 913 is 3.

Remember point 2, If the last digit of the perfect cube = 3, the last digit of the cube root = 7

__Hence the right most digit of the cube root = 7__

**Step 3**

Take the next group which is 4 .

Find out which maximum cube we can subtract from 4 such that the result ≥ 0.

We can subtract 1^{3} = 1 from 4 because 4 - 1 = 3 (If we subtract 2^{3} = 8 from 4, 4 – 8 = -4 which is < 0)

__Hence the left neighbor digit of the answer = 1. __

__i.e., answer = 17__

**Step 1 **

Identify the last three digits and make groups of three three digits from right side. i.e., 804357 can be written as

804, 357

**Step 2**

Take the last group which is 357. The last digit of 357 is 7.

Remember point 2, If the last digit of the perfect cube = 7, the last digit of the cube root = 3

__Hence the right most digit of the cube root = 3__

**Step 3**

Take the next group which is 804 .
Find out which maximum cube we can subtract from 4 such that the result ≥ 0.
We can subtract 9^{3} = 729 from 804 because 804 - 729 = 75 (If we subtract 10^{3} = 1000 from 729, 729 – 1000 = -271 which is < 0)

__Hence the left neighbor digit of the answer = 9 __

__i.e., answer = 93__

process is all same u have to solve unit digit rule as above then neglect last 3 digits and find the no whose cube value is nearest to remaining 7 digits.

if u cant then do again or reply back.

Post Your Comment