Question

нужно освободиться от иррациональности в знаменателе

Answer 1

$a) frac{5}{3 sqrt{10} } = frac{5 sqrt{10} }{3*10}= frac{5 sqrt{10} }{30} = frac{ sqrt{10} }{6} \ b) frac{8}{ sqrt{6} + sqrt{2} }= frac{8( sqrt{6}- sqrt{2} )}{6-2} = frac{8( sqrt{6}- sqrt{2} )}{4}=2 sqrt{6} -2 sqrt{2}$

Answer 2

$frac{5}{3sqrt{10}}=frac{5sqrt{10}}{3sqrt{10}sqrt{10}}=frac{5sqrt{10}}{3*10}=frac{5sqrt{10}}{30}=frac{sqrt{10}}{6} \ \ \ frac{8}{sqrt{6}+sqrt{2}}=frac{8(sqrt{6}-sqrt{2})}{(sqrt{6}+sqrt{2})(sqrt{6}-sqrt{2})}=frac{8(sqrt{6}-sqrt{2})}{(sqrt{6})^2-(sqrt{2})^2}=frac{8(sqrt{6}-sqrt{2})}{6-2}= \ =frac{8(sqrt{6}-sqrt{2})}{4}=2(sqrt{6}-sqrt{2})$