# NCERT Class 8 Mathematics Solutions: Chapter 7 – Cubes and Cube Roots Exercise 7.1 Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question: 1** Which of the following numbers are not perfect cubes:

(i) 216

(ii) 128

(iii) 1000

(iv) 100

(v) 46656

(iv) 100

**Answer**:

**(i) 216**

2 | 216 |

2 | 108 |

2 | 54 |

3 | 27 |

3 | 9 |

3 | 3 |

1 |

Prime factors of 216 =

Here all factors are in groups of 3՚s (in triplets)

Therefore, 216 is a perfect cube number.

**(ii) 128**

2 | 128 |

2 | 64 |

2 | 32 |

2 | 16 |

2 | 8 |

2 | 4 |

2 | 2 |

1 |

Prime factors of

Here one factor 2 does not appear in a 3՚s group.

Therefore, 128 is not a perfect cube.

**(iii) 1000**

2 | 1000 |

2 | 500 |

2 | 250 |

5 | 125 |

5 | 25 |

5 | 5 |

1 |

Prime factors of 1000

Here all factors appear in 3՚s group.

Therefore, 1000 is not a perfect cube.

**(iv) 100**

2 | 100 |

2 | 50 |

5 | 25 |

5 | 5 |

1 |

Prime factors of 100

Here all factors do not appear in 3՚s group.

Therefore, 100 is not a perfect cube.

**(v) 46656**

2 | 46656 |

2 | 23328 |

2 | 11664 |

2 | 5832 |

2 | 2916 |

2 | 1458 |

3 | 729 |

3 | 243 |

3 | 81 |

3 | 27 |

3 | 9 |

3 | 3 |

1 |

Prime factors of

Here, all factors appear in 3՚s group.

Therefore, 46656 is a perfect cube.