Question

Rút gọn các biểu thức :

\(a,\sqrt{11-2\sqrt{10}}\)

b, \(\sqrt{21-6\sqrt{6}}\)

Answer 1

a, \(\sqrt{11-2\sqrt{10}}\) = \(\sqrt{1-2\sqrt{10}+\sqrt{10}^2}\) = \(\sqrt{\left(1-\sqrt{10}\right)^2}\)

= \(\left|1-\sqrt{10}\right|\)

= \(\sqrt{10}-1\)

b, \(\sqrt{21-6\sqrt{6}}\) = \(\sqrt{\left(3\sqrt{2}\right)^2-2\cdot3\cdot\sqrt{2}\cdot\sqrt{3}+\sqrt{3}^2}\)

= \(\sqrt{\left(3\sqrt{2}-\sqrt{3}\right)^2}\)

= \(\left|3\sqrt{2}-\sqrt{3}\right|\)

= \(3\sqrt{2}\) - \(\sqrt{3}\)