Question

Помогите решить 8, 9, 10

Answer 1

Решение смотри в приложении

Answer 2

$8) (5+17 ^{ frac{1}{2} } ) ^{- frac{1}{3} } :(5- sqrt{17} ) ^{ frac{1}{3} } =(5+ sqrt{17} ) ^{- frac{1}{3} } :(5- sqrt{17} ) ^{ frac{1}{3} } = frac{1}{(5+ sqrt{17} ) ^{ frac{1}{3} } } : \ \ :(5- sqrt{17} ) ^{ frac{1}{3} } = frac{1}{(5+ sqrt{17} ) ^{ frac{1}{3} } } * frac{1}{(5- sqrt{17} ) ^{ frac{1}{3} } } = frac{1}{(25-17) ^{ frac{1}{3} } } = frac{1}{ sqrt[3]{8} } = frac{1}{2}$


$9) sqrt{ frac{ sqrt{56 ^{2} -46 ^{2} } }{0.25* sqrt{10} } } = sqrt{ frac{ sqrt{(56-46)(56+46)} }{0.25* sqrt{10} } } = sqrt{ frac{ sqrt{10*102} }{0.25* sqrt{10} } } = sqrt{ frac{ sqrt{10} * sqrt{102} }{0.25* sqrt{10} } } = \ \ = sqrt{ frac{ sqrt{102} }{0.25} } = sqrt{ frac{ sqrt{102} }{ frac{1}{4} } } = sqrt{4 sqrt{102} } =2 sqrt[4]{102}$


$10) frac{7( sqrt{5} - sqrt{3} ) ^{2} }{20(2+ sqrt[4]{15})(2- sqrt[4]{15}) } = frac{7(5+3-2 sqrt{15}) }{20(4- sqrt[2]{15}) } = frac{7(8-2 sqrt{15}) }{20(4- sqrt{15} )} = frac{7*2(4- sqrt{15}) }{20(4- sqrt{15}) } = frac{7*2}{20} = \\= frac{7}{10}=0.7$