Question

Помогите пожалуйста Вычислить

Answer 1

$sqrt{3 sqrt{5} }*sqrt[4]{1125}:( sqrt[3]{5}* sqrt{5 sqrt[3]{5} })=\\=3^{1/2}*(5^{1/2})^{1/2}*(5^3*3^2)^{1/4}:(5^{1/3}*5^{1/2}*(5^{1/3})^{1/2})=\\=3^{1/2}*5^{1/4}*5^{3/4}*3^{1/2}:(5^{1/3}*5^{1/2}*5^{1/6})=3*5:5=3$

$sqrt{5 sqrt{5} }: sqrt{ sqrt[3]{5 sqrt{5}} * sqrt[4]{5 sqrt[3]{5}}}=\\=5^{1/2}*(5^{1/2})^{1/2}:((5^{1/3})^{1/2}*((5^{1/2})^{1/3})^{1/2}*(5^{1/4})^{1/2}*((5^{1/3})^{1/4})^{1/2})\\=5^{1/2}*5^{1/4}:(5^{1/6}*5^{1/12}*5^{1/8}*5^{1/24})=\\=5^{3/4}:5^{(4+2+3+1)/24}=5^{3/4}:5^{10/24}=5^{3/4}:5^{5/12}=\\=5^{9/12 -5/12}=5^{4/12}=5^{1/3}= sqrt[3]{5}$