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Which of the following are cubes of an odd number

216, 729, 3375, 8000, 125, 343, 4096 and 9261.

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#### Solution

∵ 216 = 2 x 2 x 2 x 3 x 3 x 3

2 | 216 |

2 | 108 |

2 | 54 |

3 | 27 |

3 | 9 |

3 | 3 |

1 |

= (2)^{3} x (3)^{3}

= (6)^{3}

∵ 729 = 3 x 3 x 3 x 3 x 3 x 3

3 | 729 |

3 | 243 |

3 | 81 |

3 | 27 |

3 | 9 |

3 | 3 |

1 |

= (3)^{3} x (3)^{3}

= (9)^{3}

∵ 3375 = 5 x 5 x 5 x 3 x 3 x 3

5 | 3375 |

5 | 675 |

5 | 135 |

3 | 27 |

3 | 9 |

3 | 3 |

1 |

= (5)^{3} x (3)^{3}

= (15)^{3}

∵ 8000 = 20 x 20 x 20

= (20)^{3}

5 | 125 |

5 | 25 |

5 | 5 |

1 |

125 = 5 x 5 x 5

= (5)^{3}

∵ 343 = 7 x 7 x 7

= (7)^{3}

7 | 343 |

7 | 49 |

7 | 7 |

1 |

∵ 4096 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

2 | 4096 |

2 | 2048 |

2 | 1024 |

2 | 512 |

2 | 256 |

2 | 128 |

2 | 64 |

2 | 32 |

2 | 16 |

2 | 8 |

2 | 4 |

2 | 2 |

1 |

= (2)^{3} x (2)^{3} x (2)^{3} x (2)^{3}

=(16)^{3}

Cubes of an odd number are 729, 3375, 125, 343, 9261.

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