Which of the following are perfect cubes?
1. 400
2. 3375

Given: 

Given numbers are 400 and 3375.

To check: 

Here, we have to check if 400 and 3375 are perfect cubes or not.

Solution:

Checking if 400 is a perfect cube or not by using prime factorization method;

Prime factorization of $400 = 2 \times2 \times 2 \times 2 \times 5 \times 5$

In prime factorization of 400, factors 2 and 5 occur four times and 2 times respectively. But for a perfect cube every prime factor should occur in a multiple of three (three, six, nine ... and so on). 

So, we can clearly see from the factors that 400 is not a perfect cube.

Checking if 3375 is a perfect cube or not by using prime factorization method;

Prime factorization of $3375 = 3 \times3 \times 3 \times 5 \times 5 \times 5$

In prime factorization of 3375, factors 3 and 5 occur three times each.

For a perfect cube every prime factor should occur in a multiple of three (three, six, nine ... and so on). 

So, we can clearly see from the factors that 3375 is a perfect cube.