Question

Упростите выражение

$frac{5}{4+sqrt{11}}+frac{8}{sqrt{19}-sqrt{11}}-frac{10}{sqrt{19}+3}$

Вычислите :

$9^{frac{3}{2}}+27^{frac{2}{3}}-(frac{1}{16})^{-frac{3}{4}}$

Answer 1

$frac{5}{4+sqrt{11}}+frac{8}{sqrt{19}-sqrt{11}}-frac{10}{sqrt{19}+3}=frac{5(4-sqrt{11})}{(4+sqrt{11})(4-sqrt{11})}+frac{8(sqrt{19}+sqrt{11})}{(sqrt{19}-sqrt{11})(sqrt{19}+sqrt{11})}-frac{10(sqrt{19}-3)}{(sqrt{19}+3)(sqrt{19}-3)}=frac{5(4-sqrt{11})}{5}+frac{8(sqrt{19}+sqrt{11})}{8}-frac{10(sqrt{19}-3)}{10}=4-sqrt{11}+sqrt{19}+sqrt{11}-sqrt{19}+3=4+3=7$

 

$9^{frac{3}{2}}+27^{frac{2}{3}}-(frac{1}{16})^{-frac{3}{4}}=9^{frac{3}{2}}+27^{frac{2}{3}}-16^{frac{3}{4}}=sqrt[2]{9^3} +sqrt[3]{27^2} -sqrt[4]{16^3} =sqrt[2]{9^3} +sqrt[3]{27^2} -sqrt[4]{16^3} =3^3+3^2-2^3=27+9-8=28$

Answer 2

вложил решение ниже.....