Nth Root of Integer is Integer or Irrational/Historical Note

Historical Note on Nth Root of Integer is Integer or Irrational
The fact that the Square Root of 2 is Irrational was known to.

proved that the square roots of the natural numbers from $3$ to $17$, except for $4$, $9$ and $16$, are irrational.

He clearly did not have a general proof of this phenomenon.