Question

a,\(\left(\sqrt{27}-\sqrt{12}-\sqrt{108}-\sqrt{192}\right):\sqrt{3}\)

b,\(\frac{\sqrt{2}-\sqrt{6}}{1-\sqrt{3}}\frac{3+2\sqrt{7}}{1+\sqrt{3}}\)

c,(\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)

Answer 1

a) \(\left(\sqrt{27}-\sqrt{12}-\sqrt{108}-\sqrt{192}\right):\sqrt{3}=\left(3\sqrt{3}-2\sqrt{3}-6\sqrt{3}-8\sqrt{3}\right):\sqrt{3}=\left(-13\sqrt{3}\right):\sqrt{3}=-13\sqrt{3}.\frac{1}{\sqrt{3}}=-13\)

c) \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(2\sqrt{6}-3\right)^2}=\left|3-\sqrt{6}\right|+\left|2\sqrt{6}-3\right|=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)

Answer 2

a, \(=\left(3\sqrt{3}-2\sqrt{3}-6\sqrt{3}-8\sqrt{3}\right):\sqrt{3}\)

\(=\frac{-13\sqrt{3}}{\sqrt{3}}=-13\)

b, \(=\frac{\sqrt{2}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}.\frac{3+2\sqrt{7}}{1+\sqrt{3}}\)

\(=\frac{\sqrt{2}\left(3+2\sqrt{7}\right)}{1+\sqrt{3}}\)

c, \(=\sqrt{6-6\sqrt{6} +9}+\sqrt{24-2.2\sqrt{6}.3+9}\)

\(=\sqrt{\left(\sqrt{6}-3\right)^2}+\sqrt{\left(2\sqrt{6}-3\right)^2}\)

\(=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)