[tex]a)~~3\sqrt{11-\dfrac{\sqrt{11} }{3} } =3\sqrt{\dfrac{33-\sqrt{11} }{3} } =\sqrt{3^{2} \cdot (\dfrac{33-\sqrt{11} }{3} )} =\sqrt{9 \cdot (\dfrac{33-\sqrt{11} }{3} )} =\sqrt{3\cdot (33-\sqrt{11} )} =\sqrt{99-3\sqrt{11} }[/tex]
[tex]b)~~\dfrac{\sqrt{2} }{5} +\dfrac{\sqrt{2} }{10}=\dfrac{2\sqrt{2} }{10}+\dfrac{\sqrt{2} }{10}=\dfrac{2\sqrt{2}+\sqrt{2} }{10}=\dfrac{3\sqrt{2} }{10}[/tex]
[tex]c)~~5\sqrt{13} \cdot (-0,4)=5\sqrt{13} \cdot (-\dfrac{4}{10} )= 5\sqrt{13} \cdot (-\dfrac{2}{5} ) =-2\sqrt{13}[/tex]
[tex]d)~~1,2\sqrt{10} \cdot 2\sqrt{10} =\dfrac{12}{10} \cdot 2\sqrt{10\cdot 10} =\dfrac{24}{10}\cdot \sqrt{10^{2} } =\dfrac{24}{10}\cdot 10=24\\[/tex]
[tex]e)~~\dfrac{5\sqrt{7} -10\sqrt{3} }{5} =\dfrac{5\cdot (\sqrt{7} -2\sqrt{3}) }{5} =\sqrt{7} -2\sqrt{3}[/tex]
[tex]f)~~\dfrac{5}{6} \sqrt{3} \cdot \dfrac{3}{2} =\dfrac{5}{6} \cdot \dfrac{3}{2} \sqrt{3} =\dfrac{5}{4} \sqrt{3} =\dfrac{5\sqrt{3} }{4}[/tex]
