[tex]\displaystyle
1)
\sqrt{ \frac{225}{16}} + \left( \frac{3 \sqrt{5} }{5} - \frac{3 \sqrt{5} }{10} \right) \times \frac{\sqrt{5}}{3} = \\ \\
=\sqrt{ \frac{15^2}{4^2}} + \left( \frac{6 \sqrt{5} }{10} - \frac{3 \sqrt{5} }{10} \right) \times \frac{\sqrt{5}}{3} = \\ \\
= \frac{15}{4} + \frac{6 \sqrt{5}- 3 \sqrt{5} }{10} \times \frac{\sqrt{5}}{3} = \\ \\
= \frac{15}{4} + \frac{3 \sqrt{5} }{10} \times \frac{\sqrt{5}}{3} =
[/tex]
[tex]\displaystyle
= \frac{15}{4} + \frac{3 \sqrt{5} \times \sqrt{5} }{10\times 3} = \\ \\
= \frac{15}{4} + \frac{3 \times 5 }{10\times 3} = \\ \\
= \frac{15}{4} + \frac{1 }{2} = \frac{15}{4} + \frac{2 }{4} = \boxed{\frac{17}{4} }[/tex]
[tex]2) \displaystyle \\
\left( \frac{9}{ \sqrt{3} } -2 \sqrt{3}\right) \times \frac{ \sqrt{3}}{4} - \sqrt{ \frac{169}{16}}= \\ \\
= \left( \frac{9\sqrt{3}}{ 3 } -2 \sqrt{3}\right) \times \frac{ \sqrt{3}}{4} - \sqrt{ \frac{13^2}{4^2}}= \\ \\
= \left( 3\sqrt{3} -2 \sqrt{3}\right) \times \frac{ \sqrt{3}}{4} - \frac{13}{4}= \\ \\
= \sqrt{3} \times \frac{ \sqrt{3}}{4} - \frac{13}{4}=\frac{ 3}{4} - \frac{13}{4}=- \frac{10}{4}=\boxed{- \frac{5}{2}}
[/tex]
