Question

solve this question please (question. 22)

Answer 1

$\frac{ \sqrt{5} - 2 \sqrt{2} }{ \sqrt{20} + \sqrt{32} } \\ = \frac{( \sqrt{5} - 2 \sqrt{2} )( \sqrt{20} - \sqrt{32} )}{( \sqrt{20} + \sqrt{32} )( \sqrt{20} - \sqrt{32} )} \\ = \frac{ \sqrt{5} ( \sqrt{20} - \sqrt{32}) - 2 \sqrt{2} ( \sqrt{20} - \sqrt{32}) }{ { (\sqrt{20}) }^{2} - ({ \sqrt{32} )}^{2} } \\ = \frac{ \sqrt{100} - \sqrt{160} - 2 \sqrt{40} + 2 \sqrt{64} }{20 - 32} \\ = \frac{10 - 4 \sqrt{10} - 4 \sqrt{10} + 16}{ - 12} \\ = \frac{4 \sqrt{10} - 13}{6}$