Question

Избавьтесь от иррациональности в знаменателе 

1)

$frac{15}{2sqrt{6}}$

2) 

$frac{1}{sqrt{14}+sqrt{21}+sqrt{15}+sqrt{10}}$

3)

$frac{3}{3+sqrt{2}-sqrt{3}}$

Answer 1

$frac{15}{2sqrt{6}}=frac{15sqrt{6}}{2sqrt{6}sqrt{6}}=frac{15sqrt{6}}{12}=frac{5sqrt{6}}{4}$

$frac{1}{sqrt{14}+sqrt{21}+sqrt{15}+sqrt{10}}=frac{1}{sqrt{2}sqrt{7}+sqrt{3}sqrt{7}+sqrt{3}sqrt{5}+sqrt{2}sqrt{5}}=frac{1}{sqrt{7}(sqrt{2}+sqrt{3})+sqrt{5}(sqrt{2}+sqrt{3})}=frac{1}{(sqrt{2}+sqrt{3})(sqrt{7}+sqrt{5})}=frac{(sqrt{2}-sqrt{3})(sqrt{7}-sqrt{5})}{(sqrt{2}+sqrt{3})(sqrt{7}+sqrt{5})(sqrt{2}-sqrt{3})(sqrt{7}-sqrt{5})}=frac{(sqrt{2}-sqrt{3})(sqrt{7}-sqrt{5})}{(2-3)(7-5)}=-frac{(sqrt{2}-sqrt{3})(sqrt{7}-sqrt{5})}{2}$