[tex]\frac{512^2+32\cdot10^5+25^5}{64^2+4\cdot6^5+9^5}=\frac{(2^9)^2+2^5\cdot(2\cdot5)^5+(5^2)^5}{(2^6)^2+2^2\cdot(2\cdot3)^5+(3^2)^5}=[/tex]
[tex]\frac{(2^9)^2+2^5\cdot2^5\cdot5^5+(5^5)^2}{(2^6)^2+2^2\cdot2^5\cdot3^5+(3^5)^2}=\frac{(2^9)^2+2\cdot2^9\cdot5^5+(5^5)^2}{(2^6)^2+2\cdot2^6\cdot3^5+(3^5)^2}=[/tex]
[tex]\frac{(2^9+5^5)^2}{(2^6+3^5)^2}= \left(\frac{2^9+5^5}{2^6+3^5} \right)^2[/tex]
Nie jest kwadratem liczby naturalnej (jest kwadratem liczby wymiernej)
