Following a few simple steps you will be able to instantly calculate the **fifth 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 fifth powers of numbers 0 to 9, which are shown in the table below. You also need to consider the last digit of each fifth power.

Number | 5th Power | Last Digit |
---|---|---|

0 | 0 | 0 |

1 | 1 | 1 |

2 | 32 | 2 |

3 | 243 | 3 |

4 | 1024 | 4 |

5 | 3125 | 5 |

6 | 7776 | 6 |

7 | 16807 | 7 |

8 | 32768 | 8 |

9 | 59049 | 9 |

Note how the **last digit** of every fifth power **ends with the original number**.

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

Now consider the **last digit** of the number called out by the spectator. This is the **last digit **of your answer (see table above).

Spectator calls 1073741824

- Ignore last five digits = 10737
- Lower (or equal) fifth power = 7776
- Fifth root of 7776 is 6 = first digit of answer
- Last digit of spectator's call is 4 = last digit of answer
- Therefore the fifth root of 1073741824 is 64

Spectator calls 130691232

- Ignore last five digits = 1306
- Lower (or equal) fifth power = 1024
- Fifth root of 1024 is 4 = first digit of answer
- Last digit of spectator's call is 2 = last digit of answer
- Therefore the fifth root of 130691232 is 42

Called Fifth Power | Ignore Last Five |
Lower (or =) Power | First Digit (F) | Last Digit of Call | Last Digit (S) | Fifth Root = FS |
---|---|---|---|---|---|---|

248832 | 2 | 1 | 1 | 2 | 2 | 12 |

17210368 | 172 | 32 | 2 | 8 | 8 | 28 |

69343957 | 693 | 243 | 3 | 7 | 7 | 37 |

282475249 | 2824 | 1024 | 4 | 9 | 9 | 49 |

418195493 | 4181 | 3125 | 5 | 3 | 3 | 53 |

777600000 | 7776 | 7776 | 6 | 0 | 0 | 60 |

1804229351 | 18042 | 16807 | 7 | 1 | 1 | 71 |

4704270176 | 47042 | 32768 | 8 | 6 | 6 | 86 |

7339040224 | 73390 | 59049 | 9 | 4 | 4 | 94 |

Before you try this out on your friends, you should practice until you can calculate the fifth 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 Fifth Root Tester shown below.

## Fifth Root Tester |
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