Question

a.    \(\dfrac{1}{3}.\sqrt{18}-\sqrt{192}-\dfrac{\sqrt{33}}{\sqrt{11}}+3\sqrt{5\dfrac{1}{3}}\)

b.     \(\sqrt{\left(2\sqrt{3}-5\right)^2}-2\sqrt{7+4\sqrt{3}}\)

Answer 1

a: \(\dfrac{1}{3}\cdot\sqrt{18}-\sqrt{192}-\dfrac{\sqrt{33}}{\sqrt{11}}+3\cdot\sqrt{5\dfrac{1}{3}}\)

\(=\dfrac{1}{3}\cdot3\sqrt{2}-8\sqrt{3}-\sqrt{3}+3\cdot\dfrac{4}{\sqrt{3}}\)

\(=\sqrt{2}-7\sqrt{3}+4\sqrt{3}\)

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

b: Ta có: \(\sqrt{\left(2\sqrt{3}-5\right)^2}-2\cdot\sqrt{7+4\sqrt{3}}\)

\(=5-2\sqrt{3}-2\cdot\left(2+\sqrt{3}\right)\)

\(=5-2\sqrt{3}-4-2\sqrt{3}\)

\(=-4\sqrt{3}+1\)