Question

Rationalize the following

Answer 1

Answer:

1/5+2+3

1/10 is the answer

Answer 2

Answer:

$\frac{ 1 }{ (\sqrt{5} + \sqrt{2}) + \sqrt{3} } \\ = \frac{ 1 }{ (\sqrt{5} + \sqrt{2}) + \sqrt{3} } \times \frac{(\sqrt{5} + \sqrt{2}) - \sqrt{3}}{ (\sqrt{5} + \sqrt{2}) - \sqrt{3} } \\ = \frac{(\sqrt{5} + \sqrt{2}) - \sqrt{3}}{ {( \sqrt{5} + \sqrt{2}) }^{2} - 3} \\ = \frac{2 \sqrt{2} }{5 + 2 + 2 \sqrt{10} - 3} \\ = \frac{2 \sqrt{2} }{4 + 2 \sqrt{10} } \\ = \frac{ \sqrt{2} }{2 + \sqrt{10} }$