\(\sqrt{21-8\sqrt{5}}-\dfrac{11}{4-\sqrt{5}}+\sqrt{1\dfrac{4}{5}}\)
\(=\sqrt{4^2-2\cdot4\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}-\dfrac{11\left(4+\sqrt{5}\right)}{\left(4-\sqrt{5}\right)\left(4+\sqrt{5}\right)}+\sqrt{\dfrac{9}{5}}\)
\(=\sqrt{\left(4-\sqrt{5}\right)^2}-\dfrac{11\left(4+\sqrt{5}\right)}{16-5}+\dfrac{3}{\sqrt{5}}\)
\(=4-\sqrt{5}-\dfrac{11\left(4+\sqrt{5}\right)}{11}+\dfrac{3}{\sqrt{5}}\)
\(=4-\sqrt{5}-4-\sqrt{5}+\dfrac{3}{\sqrt{5}}\)
\(=-2\sqrt{5}+\dfrac{3}{\sqrt{5}}\)
\(=\dfrac{-7}{\sqrt{5}}\)
\(=\dfrac{-7\sqrt{5}}{5}\left(đpcm\right)\)
\(\sqrt{21-8\sqrt{5}}-\dfrac{11}{4-\sqrt{5}}+\sqrt{1\dfrac{4}{5}}\)
\(=\sqrt{\left(4-\sqrt{5}\right)^2}-\dfrac{11\left(4+\sqrt{5}\right)}{16-5}+\sqrt{\dfrac{9}{5}}\)
\(=4-\sqrt{5}-4-\sqrt{5}+\dfrac{3\sqrt{5}}{5}=\dfrac{3\sqrt{5}}{5}-2\sqrt{5}=-\dfrac{7}{5}\sqrt{5}\)
