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Q.

Find the smallest number by which 192 must be divided to obtain a perfect cube.

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a

9

b

3

c

6

d

7

answer is B.

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Detailed Solution

192=2×2×2×2×2×2×3

Here, 3 is left after grouping in triplets. So, 192 is not a perfect cube. 

In the factorisation 3 appears only one time. If we divide the number by 3, then it will become a perfect cube.

So, 192÷3=2×2×2×2×2×2=64 is a perfect cube.
Hence, the smallest natural number by which 192 should be divided to make it a perfect cube is 3.

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