Question

[Gia Bảo Hà Đình]

tính

\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}-\sqrt{2}\)

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Answer 1

[ILoveMath]

\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}-\sqrt{2}\)

\(=\dfrac{\sqrt{8-2\sqrt{7}}}{\sqrt{2}}-\dfrac{\sqrt{8+2\sqrt{7}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{7-2\sqrt{7}.1+1}}{\sqrt{2}}-\dfrac{\sqrt{7+2\sqrt{7}.1+1}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{7}-1-\sqrt{7}-1}{\sqrt{2}}\)

\(=-\dfrac{2}{\sqrt{2}}\)

\(=-\sqrt{2}\)