Question

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

Answer 1

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3072=2×2×2×2×2×2×2×2×2×2×3

Lets group the Factors into the Triplets Form

3072=(2×2×2×2)×(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.

Factor = 2×2×3×3 = 36

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

Answer 2

Answer:

36

Step-by-step explanation:

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

3072÷2=1536

1536÷2=768

768÷2=384

384÷2=192

192÷2=96

96÷2=48

48÷2=24

24÷2=12

12÷2=6

6÷2=3

3÷3=1

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.

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