Transform in a sum of simple radicals, please!

[Gilmar]

Transform in a sum of simple radicals, please!

[tex]\sqrt[3]{10+\sqrt[2]{108}}[/tex]

[martosss]

Transform in a sum of simple radicals, please!

[tex]\sqrt[3]{10+\sqrt[2]{108}}[/tex]

[tex]\sqrt[3]{10+\sqrt[2]{108}}=\sqrt[3]{10+12\sqrt3}=[/tex]

[tex]=\sqrt[3]{1+3*1^2*\sqrt{3}+3*1*(\sqrt{3})^2+(\sqrt{3})^3}=[/tex]

[tex]=\sqrt[3]{(1+\sqrt{3})^3}=1+\sqrt3[/tex]

[martosss]

When you see something like that - it has a root and a sum in it - the purpose is to and make it a cube, or a swuare of something, depending n the type of the radical