Question

√(3+2×√(2))+√(6−4×√(2)) demonstration ca e rational​

Answer 1

$\sqrt{3+2\sqrt{2}}+\sqrt{6-4\sqrt{2}}=\sqrt{(1+\sqrt{2})^2}+\sqrt{(2-\sqrt{2})^2}=$

$=|1+\sqrt{2}| + |2-\sqrt{2}| = 1+\sqrt{2}+2-\sqrt{2} = 3\in \mathbb{Q}$