a)
[tex] \sqrt{ \frac{7}{9} } = \frac{ \sqrt{7} }{ \sqrt{9} } = \frac{ \sqrt{7} }{ \sqrt{ {3}^{2} } } = \frac{ \sqrt{7} }{3} [/tex]
b)
[tex] \sqrt{ \frac{13}{8} } = \frac{ \sqrt{13} }{ \sqrt{8} } = \frac{ \sqrt{13} }{ \sqrt{ {2}^{3} } } = \frac{ \sqrt{13} }{2 \sqrt{2} } [/tex]
d)
[tex] \sqrt{ \frac{ {2}^{5} }{ {3}^{4} } } = \frac{ \sqrt{ {2}^{5} } }{ \sqrt{ {3}^{4} } } = \frac{2 \times 2 \sqrt{2} }{3 \times 3} = \frac{4 \sqrt{2} }{9} [/tex]
e)
[tex] \sqrt{ \frac{ {3}^{7} }{2 \times {5}^{3} } } = \frac{ \sqrt{ {3}^{7} } }{2 \times {5}^{3} } = \frac{3 \times 3 \times 3 \sqrt{3} }{5 \sqrt{2 \times 5} } = \frac{27 \sqrt{3} }{5 \sqrt{10} } [/tex]
h)
[tex] \sqrt{ \frac{8}{3} } = \frac{ \sqrt{8} }{ \sqrt{3} } = \frac{ \sqrt{ {2}^{3} } }{ \sqrt{} 3} = \frac{2 \sqrt{2} }{ \sqrt{3} } [/tex]
