Question

8. Find the smallest number by which 2560 must be multiplied so that the product is a perfect
cube.
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Answer 1

Answer:

25

Step-by-step explanation:

2560=2×2×2×2×2×2×2×2×2×5 or 2^9×5

in order to get perfect cube both must have powers as a multiple of 3.2 already has power multiple of 3 so we need to multiply 5² to get a perfect cube so answer is 25

Answer 2

Answer:

Given no = 2560 . expressing into prime factors ,we have 2560 = 2×2×2×2×2×2×2×2×2×5 . since 5 left unpaired . to make perfect cube , we should multiplied 5×5=25 .2560×25 = 64000. which is a perfect cube. hence the smallest no by which 2560 must be multiplied so that product is perfect cube = 5×5=25.