Question

what is the smallest number by which 2560 must be multiply so that the product is a perfect cube?​

Answer 1

Step-by-step explanation:

Its nearest perfect cube is 2744 . It is the cube of 14.

To get 2744, Let we have to multiply with X.

then, 2560 × X = 2744

=> X = 2744/2560 = 1.072

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but, the smallest which can be multiplied is NOT DEFINED. Because there can be numbers which are negative and can be multiplied with 2560 to get any perfect cube.

Answer 2

Solution=Take Prime factors of 2560.

i.e.2560=2×2×2×2×2×2×2×2×2×5.

The product has 3 sets of 2^3 and a 5.

Clearily to make it perfect cube,it must be multiplied by 5×5 i.e. 25.