a) Ta có: \(\sqrt{8-\sqrt{55}}\)
\(=\frac{\sqrt{16-2\sqrt{55}}}{\sqrt{2}}\)
\(=\frac{\sqrt{11-2\cdot\sqrt{11}\cdot\sqrt{5}+5}}{\sqrt{2}}\)
\(=\frac{\sqrt{\left(\sqrt{11}-\sqrt{5}\right)^2}}{\sqrt{2}}\)
\(=\frac{\sqrt{11}-\sqrt{5}}{\sqrt{2}}\)
b) Ta có: \(\sqrt{7-\sqrt{33}}\)
\(=\frac{\sqrt{14-2\sqrt{33}}}{\sqrt{2}}\)
\(=\frac{\sqrt{11-2\cdot\sqrt{11}\cdot\sqrt{3}+3}}{\sqrt{2}}\)
\(=\frac{\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}}{\sqrt{2}}\)
\(=\frac{\sqrt{11}-\sqrt{3}}{\sqrt{2}}\)
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