Lời giải:
a)
\(\sqrt{3-\sqrt{5}}+\sqrt{7-3\sqrt{5}}=\sqrt{\frac{6-2\sqrt{5}}{2}}+\sqrt{\frac{14-6\sqrt{5}}{2}}\)
\(=\sqrt{\frac{5+1-2\sqrt{5.1}}{2}}+\sqrt{\frac{3^2+5-2.3\sqrt{5}}{2}}\)
\(=\sqrt{\frac{(\sqrt{5}-1)^2}{2}}+\sqrt{\frac{(3-\sqrt{5})^2}{2}}\)
\(=\frac{\sqrt{5}-1}{\sqrt{2}}+\frac{3-\sqrt{5}}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}\)
b)
\(\sqrt{8-2\sqrt{7}}-\sqrt{16+5\sqrt{7}}=\sqrt{7+1-2\sqrt{7.1}}-\sqrt{\frac{32+10\sqrt{7}}{2}}\)
\(=\sqrt{(\sqrt{7}-1)^2}-\sqrt{\frac{5^2+7+2.5\sqrt{7}}{2}}\)
\(=\sqrt{(\sqrt{7}-1)^2}-\sqrt{\frac{(5+\sqrt{7})^2}{2}}=\sqrt{7}-1-\frac{5+\sqrt{7}}{\sqrt{2}}\)
\(=\frac{\sqrt{14}-\sqrt{2}-5-\sqrt{7}}{\sqrt{2}}\)
Lời giải:
a)
\(\sqrt{3-\sqrt{5}}+\sqrt{7-3\sqrt{5}}=\sqrt{\frac{6-2\sqrt{5}}{2}}+\sqrt{\frac{14-6\sqrt{5}}{2}}\)
\(=\sqrt{\frac{5+1-2\sqrt{5.1}}{2}}+\sqrt{\frac{3^2+5-2.3\sqrt{5}}{2}}\)
\(=\sqrt{\frac{(\sqrt{5}-1)^2}{2}}+\sqrt{\frac{(3-\sqrt{5})^2}{2}}\)
\(=\frac{\sqrt{5}-1}{\sqrt{2}}+\frac{3-\sqrt{5}}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}\)
b)
\(\sqrt{8-2\sqrt{7}}-\sqrt{16+5\sqrt{7}}=\sqrt{7+1-2\sqrt{7.1}}-\sqrt{\frac{32+10\sqrt{7}}{2}}\)
\(=\sqrt{(\sqrt{7}-1)^2}-\sqrt{\frac{5^2+7+2.5\sqrt{7}}{2}}\)
\(=\sqrt{(\sqrt{7}-1)^2}-\sqrt{\frac{(5+\sqrt{7})^2}{2}}=\sqrt{7}-1-\frac{5+\sqrt{7}}{\sqrt{2}}\)
\(=\frac{\sqrt{14}-\sqrt{2}-5-\sqrt{7}}{\sqrt{2}}\)
