Question

$\frac{5}{ \sqrt{7}- \sqrt{2} } + \frac{2}{3+ \sqrt{7} }$
$\sqrt{ \sqrt{5}( \sqrt{5} - \sqrt{7)} - \sqrt{7} ( \sqrt{5}- \sqrt{7)} }$

Answer 1

[tex]\frac{5}{ \sqrt{7}- \sqrt{2} } + \frac{2}{3+ \sqrt{7} }= \\ \\ \frac{ \sqrt{35}+ \sqrt{10}}{5}+ \frac{6-2 \sqrt{7}}{2}= \\ \\ \frac{2 \sqrt{35}+2 \sqrt{10}}{10} + \frac{30-10 \sqrt{7}}{10}= \\ \\ \frac{2 \sqrt{35}+2 \sqrt{10}+30-10 \sqrt{7}}{10} = \\ \\ \frac{2( \sqrt{35}+ \sqrt{10}+15-5 \sqrt{7}) }{2*5} = \\ \\ =\frac{ \sqrt{35}+ \sqrt{10}+15-5 \sqrt{7} }{5} [/tex]