rút gọn ạ
\(\dfrac{\sqrt{12}-\sqrt{16}}{\sqrt{3}-2}+\dfrac{\sqrt{21}+\sqrt{7}}{\sqrt{3}+1}+\sqrt{\left(2-\sqrt{7}\right)^2}\)
\(\dfrac{9}{\sqrt{10}-1}+\dfrac{5\sqrt{2}-\sqrt{5}}{\sqrt{5}}+\sqrt{11-2\sqrt{10}}\)
\(\dfrac{2}{\sqrt{3}-1}-\sqrt{27}+\left(\sqrt{3}+1\right)^2\)
\(\dfrac{1}{2-\sqrt{2}}-\dfrac{1}{2+\sqrt{2}}+\dfrac{\sqrt{15}-3\sqrt{3}}{3-\sqrt{5}}\)
\(\dfrac{\sqrt{12}-\sqrt{16}}{\sqrt{3}-2}+\dfrac{\sqrt{21}+\sqrt{7}}{\sqrt{3}+1}+\sqrt{\left(2-\sqrt{7}\right)^2}\)
\(=\dfrac{2\left(\sqrt{3}-2\right)}{\sqrt{3}-2}+\dfrac{\sqrt{7}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}+\left|\sqrt{7}-2\right|\)
\(=2+\sqrt{7}+\sqrt{7}-2=2\sqrt{7}\)
\(\dfrac{9}{\sqrt{10}-1}+\dfrac{5\sqrt{2}-\sqrt{5}}{\sqrt{5}}+\sqrt{11-2\sqrt{10}}\)
\(=\dfrac{9\left(\sqrt{10}+1\right)}{10-1}+\dfrac{\sqrt{5}\left(\sqrt{10}-1\right)}{\sqrt{5}}+\sqrt{10}-1\)
\(=\sqrt{10}+1+\sqrt{10}-1+\sqrt{10}-1=3\sqrt{10}-1\)
\(\dfrac{2}{\sqrt{3}-1}-\sqrt{27}+\left(\sqrt{3}+1\right)^2\)
\(=\dfrac{2\left(\sqrt{3}+1\right)}{3-1}-3\sqrt{3}+4+2\sqrt{3}\)
\(=\sqrt{3}+1-\sqrt{3}+4=1+4=5\)
\(\dfrac{1}{2-\sqrt{2}}-\dfrac{1}{2+\sqrt{2}}+\dfrac{\sqrt{15}-3\sqrt{3}}{3-\sqrt{5}}\)
\(=\dfrac{2+\sqrt{2}-2+\sqrt{2}}{4-2}-\dfrac{\sqrt{3}\left(3-\sqrt{5}\right)}{3-\sqrt{5}}\)
\(=\dfrac{2\sqrt{2}}{2}-\sqrt{3}=\sqrt{2}-\sqrt{3}\)
