Following a few simple steps you will be able to instantly calculate the **cube root** of the spectator's number.

Ask the spectator to choose any whole number less than 100 and, using a calculator, to find its cube by multiplying the number by itself, then multiplying the answer by the original number.

Alternatively, if the spectator knows how to use scientific calculator, they can enter the original number, then press the **x^y key followed by 3 and =**.

The spectator then calls out the answer, and you instantly reveal the original number (i.e., the cube root).

**Note that this method will NOT work with non-whole numbers, or with numbers greater than 99**.

To master the system you must **learn by heart** the cubes of numbers 0 to 9, which are shown in the table below. You also need to consider the last digit of each cube.

Number | Cube | Last Digit |
---|---|---|

0 | 0 | 0 |

1 | 1 | 1 |

2 | 8 | 8 |

3 | 27 | 7 |

4 | 64 | 4 |

5 | 125 | 5 |

6 | 216 | 6 |

7 | 343 | 3 |

8 | 512 | 2 |

9 | 729 | 9 |

Note how the last digit of the cubes for 0, 1, 4, 5, 6, and 9 end with the original number.

Note how the last digits for the cubes of 2 and 8 are swapped.

Note how the last digits for the cubes of 3 and 7 are swapped.

Ignore the last **three** digits of the number called out by the spectator and choose the memorised cube which is **just lower** (or equal) to the remaining number. The cube root of this is the **first digit** of your answer.

Now consider the **last digit** of the number called out by the spectator. This will indicate the **last digit **of your answer. For example, if the last digit of the number called out is 3, then the last digit of the cube root is 7 (see the last digit values in the table above).

Spectator calls 185193

- Ignore last three digits = 185
- Lower (or equal) cube = 125
- Cube root of 125 is 5 = first digit of answer
- Last digit of spectator's call = 3
- From table of cubes (shown above), when the last digit of cube is 3, the last digit of the cube root is 7
- Therefore the cube root of 185193 is 57

Spectator calls 438976

- Ignore last three digits = 438
- Lower (or equal) cube = 343
- Cube root of 343 is 7 = first digit of answer
- Last digit of spectator's call = 6
- From table of cubes (shown above), when the last digit of cube is 6, the last digit of the cube root is also 6
- Therefore the cube root of 438976 is 76

Called Cube | Ignore Last Three | Lower (or =) Cube | First Digit (F) | Last Digit of Call | Last Digit (S) | Cube Root = FS |
---|---|---|---|---|---|---|

1728 | 1 | 1 | 1 | 8 | 2 | 12 |

21952 | 21 | 8 | 2 | 2 | 8 | 28 |

50653 | 50 | 27 | 3 | 3 | 7 | 37 |

117649 | 117 | 64 | 4 | 9 | 9 | 49 |

148877 | 148 | 125 | 5 | 7 | 3 | 53 |

216000 | 216 | 216 | 6 | 0 | 0 | 60 |

357911 | 357 | 343 | 7 | 1 | 1 | 71 |

636056 | 636 | 512 | 8 | 6 | 6 | 86 |

830584 | 830 | 729 | 9 | 4 | 4 | 94 |

Before you try this out on your friends, you should practice until you can calculate the cube root instantly and without error.

If you can't do this, then **practice some more**!

To practice and assess your ability, you can use the Cube Root Tester shown below.

## Cube Root Tester |
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