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

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Rayzenask

[tex]\sqrt{3+2\sqrt{2}}+\sqrt{6-4\sqrt{2}}=\sqrt{(1+\sqrt{2})^2}+\sqrt{(2-\sqrt{2})^2}=[/tex]

[tex]=|1+\sqrt{2}| + |2-\sqrt{2}| = 1+\sqrt{2}+2-\sqrt{2} = 3\in \mathbb{Q}[/tex]

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