Question

find the smallest number by which 2560 must be multiplied so that the product is a perfect cube​

Answer 1

Take Prime factors of 2560.

2560 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5.

Now we can see that there are 3 sets of 2 cube and only one 5

Thus to nake it a perfect cube we must multiply 2560 with 5 × 5.

Hope this helps.

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Answer 2

Firstly We find the prime factorisation of 2560

2560 =2×2×2×2×2×2×2×2×2×5

From the factors, we can say that only 5 is a factor that is not occurring three times or in the multiple of it to make it a perfect cube.

So to make it a perfect cube, the above number should be multiplied with

5×5=25.

So, 25 is the required answer.

Hope it's help you