Question

D = \(\sqrt{4-\sqrt{7}}\) - \(\sqrt{4+\sqrt{7}}\) + \(\sqrt{8}\) Tìm giá trị của D

Answer 1

\(D=\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{8}=\dfrac{\sqrt{2}\left(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{8}\right)}{\sqrt{2}}=\dfrac{\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}+\sqrt{16}}{\sqrt{2}}=\dfrac{\sqrt{7-2\sqrt{7}+1}-\sqrt{7+2\sqrt{7}+1}+4}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}+4}{\sqrt{2}}=\dfrac{\left|\sqrt{7}-1\right|-\left|\sqrt{7}+1\right|+4}{\sqrt{2}}=\dfrac{\sqrt{7}-1-\sqrt{7}-1+4}{\sqrt{2}}=\dfrac{2}{\sqrt{2}}=\sqrt{2}\)