Find the sum of all positive integers less than $200$ that are both perfect squares and perfect cubes.

Step-by-step solution

1. Step 1: A number that is both a perfect square and a perfect cube must be a perfect sixth power $n^6$.
2. Step 2: Find integers $n$ such that $n^6<200$.
3. Step 3: $1^6=1$ (less than 200), $2^6=64$ (less than 200), $3^6=729$ (greater than 200).
4. Step 4: The numbers are 1 and 64.
5. Step 5: Sum them: $1+64=65$.

Concept tested: perfect sixth powers

Published 13 October 2026 · How this solution was prepared and checked