Question

Ayudenme con 5 ejercicios similares a esta fórmula de radicales..

Answer 1

$\sqrt{ \sqrt[3]{ \sqrt[4]{2} } } = \sqrt[2*3*4]{2} = \sqrt[24]{2} =1,029$

$\sqrt{2 \sqrt[3]{2 \sqrt[4]{2} } } = \sqrt{\sqrt[3]{2^{3}*2 \sqrt[4]{2}}}$ = $\sqrt{\sqrt[3]{2^{4} \sqrt[4]{2}}} = \sqrt{\sqrt[3]{ \sqrt[4]{(2^{4})^{4}*2}}}$ = $= \sqrt{ \sqrt[3]{ \sqrt[4]{2^{16}*2}}} = \sqrt[2*3*4]{2^{17}}$ = $\sqrt[24]{2^{17}} = \sqrt[24]{131072}=1,6339$

$\sqrt[5]{ \sqrt[2]{ \sqrt[3]{25}}} = \sqrt[5*2*3]{25}= \sqrt[30]{25} =1,113$

$\sqrt[5]{ \sqrt[4]{ \sqrt[2]{5^{3}} } } = \sqrt[5*4*2]{125} = \sqrt[40]{125} =1,1283$

$\sqrt{2 \sqrt[4]{7 \sqrt[3]{12} } } = \sqrt{ \sqrt[4]{2^{4}*7 \sqrt[3]{12} } } =$=$\sqrt{ \sqrt[4]{ \sqrt[3]{(2^{4})^{3}*7^{3}*12}}}= \sqrt[2*4*3]{2^{12}*7^{3}*12}$=$\sqrt[24]{4096*343*12}= \sqrt[24]{16859136}=2,00041$