Question

Rút gọn:

D= \(\left(\sqrt{3}-1\right)\) . \(\sqrt{6+2\sqrt{2}.\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18}-\sqrt{128}}}\)

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Answer 1

\(D=\left(\sqrt{3}-1\right)\cdot\sqrt{6+2\sqrt{2}\cdot\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18}-\sqrt{128}}}\\ D=\left(\sqrt{3}-1\right)\cdot\sqrt{6+2\sqrt{2}\cdot\sqrt{\sqrt{2}+2\sqrt{2}+3\sqrt{2}-8\sqrt{2}}}\\ D=\left(\sqrt{3}-1\right)\cdot\sqrt{6+2\sqrt{2}\cdot\left(-2\sqrt{2}\right)}\\ D=\left(\sqrt{3}-1\right)\cdot\sqrt{6+\sqrt{12}\cdot\left(-\sqrt{12}\right)}\\ D=\left(\sqrt{3}-1\right)\cdot\sqrt{6+\left(-12\right)}\\ D=\left(\sqrt{3}-1\right)\cdot\sqrt{6}\\ D=\sqrt{18}-\sqrt{6}\)