Question

Помогите решить. 
$\frac{(5 \sqrt{3}+ \sqrt{50})(5- \sqrt{24})}{ \sqrt{75}-5 \sqrt{2} }$

Answer 1

$\frac{(5 \sqrt{3}+ \sqrt{50} )(5- \sqrt{24}) }{ \sqrt{75} -5 \sqrt{2} }=\frac{5\sqrt{3} -5 \sqrt{2} }{5\sqrt{3} -5 \sqrt{2} } =1$

$\\ \\ (5 \sqrt{3} + \sqrt{50} )(5- \sqrt{24} )= \\ =25 \sqrt{3} -5 \sqrt{72} +5 \sqrt{50} - \sqrt{1200} = \\ =25 \sqrt{3} -5 \sqrt{36*2} +5 \sqrt{25*5} - \\ - \sqrt{400*3} =25 \sqrt{3} -5*6 \sqrt{2} + \\ +5*5 \sqrt{2} -20 \sqrt{3} =25 \sqrt{3} -30 \sqrt{2} + \\ +25 \sqrt{2} -20 \sqrt{3} =25 \sqrt{3} -20 \sqrt{3} + \\ +25 \sqrt{2} -30 \sqrt{2} =5 \sqrt{3} -5 \sqrt{2} \\ \\ \sqrt{75} -5 \sqrt{2} = \sqrt{25*3} -5 \sqrt{2} = \\ =5 \sqrt{3} -5 \sqrt{2}$

Answer 2

$\frac{(5 \sqrt{3}+ \sqrt{50 })(5- \sqrt{24}) }{ \sqrt{75} -5 \sqrt{2} } = \\ = \frac{(5 \sqrt{3}+5 \sqrt{2})(5-2 \sqrt{6}) }{5 \sqrt{3}-5 \sqrt{2} } } = \frac{(5 \sqrt{3}+5 \sqrt{2})^2(5-2 \sqrt{6} ) }{25*3-25*2} = \\ = \frac{(75+50 \sqrt{6}+50)(5-2 \sqrt{6} ) }{75-50} = \frac{(125+50 \sqrt{6})(5-2 \sqrt{6} ) }{25}= \\ = \frac{625-250 \sqrt{6}+250 \sqrt{6}-600 }{25}= \frac{25}{25}=1$