### Basic Cube Values

1st of all we need to remember the cubes of number ranging from 1 to 10. Below the cubes of this number is given in table form:-

Number | Cube |

1 | 1 |

2 | 8 |

3 | 27 |

4 | 64 |

5 | 125 |

6 | 216 |

7 | 343 |

8 | 512 |

9 | 729 |

10 | 1000 |

### Last Digits of Cube Roots

Another table we need to remember for evaluating cube roots is given below:-

Last digit of the cube | Last digit of the cube roots |

1 | 1 |

2 | 8 |

3 | 7 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 3 |

8 | 2 |

9 | 9 |

0 | 0 |

Now take some example:-

### Examples

*Example 1*:

*Find \( \sqrt[3]{941192}\)*

__A____nswer__: – Detailed step is given below

- 1
^{s}^{t}of all write the number as two pair of three digits each,__941____1____92__. - Since cube ends with 2 so last digit of the cube root is 8. (As given in the above table).
- Now the left pair of the number is 941. So it lies between 729(\(\sqrt[3]9\)) and 1000( \( \sqrt[3]{10}\)).
- Now out of 9and 10 smaller number is 9, so we take 9 as the left part in the answer and put it left to the 8. So final answer is
**98.**

** Example 2**:

*Find \(\sqrt[3]{1367631}\)*

__A____nswer__: Steps are given below,

- Here we have to divide the number as 1367 631 (Remember, 2 nd part always consist of last three digit number).
- Now last digit of cube is 1 so last digit of the cube root is 1. We get the extreme right part of the cube root.
- Now the left part 1367 lies between 1331( \(\sqrt[3]{11}\)) and 1728(\(\sqrt[3]{12}\)).
- So smaller number between 11 and 12 is 11. So the left part of \(\sqrt[3]{11}\). The answer is
**111.**

** Example 3**:

*Find \(\sqrt[3]{79507}\).*

__A____nswer:____ __Steps are given below,

- Here we have to divide the number as
__79 5____0____7__ - Now last digit of the cube is 7,so last digit of the cube root 3.We get the right part of the answer as 3.
- Now the left part lies between 64(\(\sqrt[3]{4}\)) and 125(\(\sqrt[3]{5}\)).
- So the smaller number between 4 and 5 is 4.
- So the answer is
**43.**

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