Question

find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
(a) 252
(b) 72
(c) 675
(d) 100

Answer 1

I give you hints, try these by yourself.
Step 1) Prime factorize the given number.( e.g. prime factorization of 20 = 5×2×2)
Step 2) Check whether each factor has a pair of or not?
Step 3) If yes then the number is perfect cube otherwise not.
Step 4) If each factor does not have a pair of three then the number is not a perfect cube.
Step 5) Multiply the number by a factor which is not in pair of three.


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