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.