+308 What is the least four-digit whole number that is both a perfect square and a perfect cube?
+26393 What is the least four-digit whole number that is both a perfect square and a perfect cube?
The number must be perfect 6th power (\(2\times 3\))
\(\begin{array}{|c|rcl|cc|} \hline n & n^6 && &\text{four-digit}\\ \hline 1 & 1^6 &=& 1 \\ 2 & 2^6 &=& 54 \\ 3 & 3^6 &=& 729 \\ 4 & 4^6 &=& 4096 & \checkmark & 4096=64^2,\ 4096=16^3 \\ 5 & 5^6 &=& 15625 \\ \hline \end{array}\)
