We suposse that [tex] \sqrt{2} + \sqrt{6} [/tex] = a is rational;
Then, [tex] ( \sqrt{2} + \sqrt{6} )^{2} = a^{2} ; [/tex]
2 + [tex] \sqrt{12} [/tex] + 6 = [tex] a^{2} [/tex];
[tex] \sqrt{12} [/tex] = [tex] a^{2} - 8;[/tex]
But [tex] \sqrt{12} [/tex] is irrational and [tex] a^{2} -8 [/tex] is rational; false;
Finally, √ 2 + √ 6 is irrational .
