Question

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

Answer 1

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

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

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

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