Answer:
See below
Step-by-step explanation:
a)
[tex] \frac{20}{ \sqrt{10} } = \frac{20 \sqrt{10} }{ \sqrt{10} \times \sqrt{10} } = \frac{20 \sqrt{10} }{10} = 2 \sqrt{10} [/tex]
b)
[tex] \frac{ \sqrt{2} }{2 \sqrt{5} - 1 } \\ \\ = \frac{ \sqrt{2} \times (2 \sqrt{5} + 1 )}{(2 \sqrt{5} - 1)(2 \sqrt{5} + 1) } \\ \\ = \frac{ \sqrt{2} \times 2 \sqrt{5} + \sqrt{2} \times 1 }{(2 \sqrt{5} ) ^{2} - (1)^{2}} \\ \\ = \frac{ 2 \sqrt{10} + \sqrt{2}}{20 - 1} \\ \\ = \frac{ 2 \sqrt{10} + \sqrt{2}}{19} \\ \\ equating \: it \: with \: \\ \frac{ a + \sqrt{b}}{c} \\ \\ a = 2 \sqrt{10} \\ \\ b = 2 \\ \\ c = 19[/tex]
