Date,
By which smallest number should 643 be
multiplied so that the product is a perfect.cube
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Answer:
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Step-by-step explanation:
648 = 2 × 2 × 2 × 3 × 3 × 3 × 3
In the prime factors, only 2 and 3 are present. 2 form a triplet (there are three 2s), while there are four 3s.To be a perfect cube, all prime factors should be in multiples of 3. Therefore, to make 648 a perfect cube, it has to be multiplied by 3 × 3 = 9 (so that there will be six 3s in total).
P.S. You can also multiply by \frac{1}{3}31 , which is smaller or by \frac{1}{648}6481 , which is even smaller, but the officially accepted answers are integers, unless they specify otherwise.
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