Question

find the smallest number by which 1280 must be divided to get perfect square find the cube root of the perfect cube so obtained

Answer 1

Answer:

1536=2×2×2×2×2×2×2×2×2×3

After grouping the prime factors in triplets, it’s seen that one factor 3 is left without grouping.

1536=(2×2×2)×(2×2×2)×(2×2×2)×3

So, in order to make it a perfect cube, it must be divided by 3.

Thus, the smallest number by which 1536 must be divided to obtain a perfect cube is 3.

Answer 2

Answer:

1280

√1280 = √(2*2*2*2*2*2*2*2*5)

√1280 =√(2*2*2*2*7)

So, 7 is left alone therefore, 7 is the smallest number to be multiplied by 1280 to make it a perfect square.

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