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# help

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What is the least four-digit whole number that is both a perfect square and a perfect cube?

Mar 13, 2020

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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 ($$2\times 3$$)

$$\begin{array}{|c|rcl|cc|} \hline n & n^6 && &\text{four-digit}\\ \hline 1 & 1^6 &=& 1 \\ 2 & 2^6 &=& 54 \\ 3 & 3^6 &=& 729 \\ 4 & 4^6 &=& 4096 & \checkmark & 4096=64^2,\ 4096=16^3 \\ 5 & 5^6 &=& 15625 \\ \hline \end{array}$$

Mar 13, 2020