Nth Root of Integer is Integer or Irrational/Historical Note
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Historical Note on Nth Root of Integer is Integer or Irrational
The fact that the Square Root of 2 is Irrational was known to Pythagoras of Samos.
Theodorus of Cyrene 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.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1 \cdotp 41421 \, 35623 \, 73095 \, 04880 \, 16887 \, 24209 \, 69807 \, 85697 \ldots$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 41421 \, 35623 \, 73095 \, 04880 \, 16887 \, 24209 \, 69807 \, 85697 \ldots$