[tex] \sqrt{2 + \frac{1}{4} } [/tex]
=
[tex] \sqrt{ \frac{8}{4} + \frac{1}{4} } = \sqrt{ \frac{9}{4} } = \frac{ \sqrt{9} }{ \sqrt{4} } = \frac{3}{2} [/tex]
[tex] \sqrt{5 + \frac{4}{9} } = \sqrt{ \frac{45}{9} + \frac{4}{9} } = \sqrt{ \frac{49}{9} } [/tex]
[tex] \frac{ \sqrt{49} }{ \sqrt{9} } = \frac{7}{3} [/tex]
[tex] \frac{3}{2} + \frac{7}{3} = \frac{9}{6} + \frac{14}{6} = \frac{23}{6} [/tex]