Question

Tính : \(\sqrt{4-\sqrt{7}-\sqrt{4+\sqrt{7}}}\)

Answer 1

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

mk chép sai đề bài ở trên nha

Answer 2

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

\(=\dfrac{\sqrt{2}.\sqrt{4-\sqrt{7}}}{\sqrt{2}}-\dfrac{\sqrt{2}.\sqrt{4+\sqrt{7}}}{\sqrt{2}}\)

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

\(=\dfrac{\sqrt{\left(\sqrt{7}-1\right)^2}}{\sqrt{2}}-\dfrac{\sqrt{\left(\sqrt{7}+1\right)^2}}{\sqrt{2}}\)

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

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