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
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.