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Q.

Which of the numbers is a perfect cube?


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a

243

b

512

c

392

d

8640 

answer is B.

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Detailed Solution

The given numbers are 243, 512, 392, 8640.
Utilizing prime factorization, express the given number as a product of the factors in the triple form.
From option 1,
⇒243=3×3×3×3×3= 3 3 × 3 2  
 From option 2,
⇒512=2×2×2×2×2×2×2×2×2= 2 3 × 2 3 × 2 3  
From option 3,
⇒392=2×2×2×7×7   From option 4,
⇒8640=2×2×2×2×2×2×3×3×3×5 ⇒ 2 3 × 2 3 × 3 3 ×5  
The number 512 is a perfect cube since there are no factors in grouping (triples) that are left over.
Thus, 512 is the ideal cube.
Therefore, option 2 is correct.
 
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