Question

By what smallest number should 12000 be nultipled so that the product becomes a perfect cube?(With appropriate Step-wise Explanation)​

Answer 1

Heya Mate! Here's you answer:

18

Step-by-step explanation:

Prime Factorization of 12000 = 3 x 2 x 2 x 2 x 2 x 2 x 5  x 5 x 5

If we add (2 x 3 x 3) in to this row, we could get the cube of (3 x 2 x 2 x 5)

ie. 60

Because to form a cube all the prime numbers present in it should be present in the quantity of 3 each, but in this case, as we can see above, only number 2 and 5 is present in the quantity of 3, the other 2 and 3 need 1 more and 2 more (respectively) of it's kind to form a trio and generate a perfect cube.

So we need to multiply it by 3 x 3 x 2 (18) to create a perfect cube

The resulting cube would be 216000 which  is the cube of 60 (60 x 60 x 60)

Hope It Helps :)

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