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Question 92

Solve the following question:

Using prime factorization, find which of the following are perfect cubes.

a) 128
b) 343
c) 729
d) 1331


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Solution

a) We have, 128=2×2×2×2×2×2×2
Since, 2 remains after grouping in triplets
So, 128 is not a perfect cube.

b) We have, 343=7×7×7
Since, the prime factors appear in triplets
So, 343 is a perfect cube.

c) We have, 729=3×3×3×3×3×3
Since, the prime factors appear in triplets
So, 729 is a perfect cube.

d) We have, 1331=11×11×11
Since, the prime factors appear in triplets.
So, 1331 is a perfect cube.


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