Question

find the smallest number by which 3072must be multiplied to obtain perfect cube​

Answer 1

Step-by-step explanation:

here is the answer of the question

Answer 2

Answer:

We have,

3072 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

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After grouping the prime factors in triplets, it’s seen that factor 2 × 3 are left ungrouped.

3072 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 2 × 3

So, in order to complete them in a group of 3’s we need the factors 2 × 2 × 3 × 3 to be multiplied.

i.e. the factor needed is 2 × 2 × 3 × 3 = 36

Thus, the smallest number which should be multiplied to 3072 in order to make it a perfect cube is 36.