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Question
999 is a perfect cube.
Options
True
False
Solution
This statement is False.
Explanation:
| 3 | 999 |
| 3 | 333 |
| 3 | 111 |
| 37 | 37 |
| 1 |
Resolving 999 into prime factors, we get
999 = 3 × 3 × 3 × 37
Grouping the factors in triples of equal factors, we get
999 = (3 × 3 × 3) × 37
Clearly, in grouping, the factor in triples of equal factors, we are left with one factor 37.
Therefore, 999 is not a perfect cube.
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Observe the following pattern:
13 = 1
13 + 23 = (1 + 2)2
13 + 23 + 33 = (1 + 2 + 3)2
Write the next three rows and calculate the value of 13 + 23 + 33 + ... + 93 + 103 by the above pattern.
Is 243 a perfect cube?
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363 × 81 is a perfect cube.
