Which of these is not a perfect cube-343-81-1331-512-

The correct option is B 81 By prime factorization, we have 343=7×7×7 1331=11×11×11 512=8×8×8 81=3×3×3×3 For a number to be a perfect cube ,each of its f ...

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Standard VIII

Mathematics

Finding Cube Roots Using Prime Factorization

Which of thes...

Question

Which of these is not a perfect cube?

343

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1331

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512

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Solution

The correct option is D
81

By prime factorization, we have

$343 = 7 \times 7 \times 7 1331 = 11 \times 11 \times 11 512 = 8 \times 8 \times 8 81 = 3 \times 3 \times 3 \times 3$

For a number to be a perfect cube ,each of its factors must be repeated thrice.
343, 1331 and 512 are the perfect cubes of 7, 11 and 8 respectively, whereas 81 is not, as 3 is repeating 4 times which is not a triplet.

81 is not a perfect cube.

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