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Which of the subsequent numbers is a perfect cube?

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121

169

196

216

answer is D.

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Detailed Solution

The given numbers are 121, 169, 196, and 216.
Find the prime factorization of 216.

2216210825432739331

Prime factorization of 216 is:

We have:

Therefore, the given number 216 is a perfect cube as its prime factors 2 and 3 occur in a triplet.
The prime factorization of

Here, the prime factors don’t occur in triplet form. So, the number 121 isn’t a perfect cube.
The prime factorization of

Here, the prime factors don’t occur in triplet form. So, the number 169 isn’t a perfect cube.
The prime factorization of

Here, the prime factors don’t occur in triplet form. So, the number 196 isn’t a perfect cube.
Therefore, the number 216 is a perfect cube of 6.
Thus, option (4) is correct

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