Question

Избавьтесь от иррациональности в знаменателе $frac{1}{sqrt{3}-sqrt{5}-2sqrt{2} }$

Answer 1

$frac{1}{sqrt3-sqrt5-2sqrt2}=frac{(sqrt3-sqrt5)+2sqrt2}{(sqrt3-sqrt5)^2-(2sqrt2)^2}=frac{sqrt3-sqrt5+2sqrt2}{(8-2sqrt{15})-8}=-frac{sqrt3-sqrt5+2sqrt2}{2sqrt{15}} =\\=-frac{(sqrt3-sqrt5+2sqrt2)cdot sqrt{15}}{30}=frac{-sqrt{3cdot 15}+sqrt{5cdot 15}-2sqrt{2cdot 15}}{30}=frac{5sqrt3-3sqrt5-2sqrt{30}}{30}$