Exercise
Simplify the expression:
\frac{1}{\sqrt[4]{2}+1}
Final Answer
Solution
\frac{1}{\sqrt[4]{2}+1}=
=\frac{1}{2^{\frac{1}{4}}+1}=
=\frac{1}{{(\sqrt{2})}^2+1}=
=\frac{{(\sqrt{2})}^2-1}{({(\sqrt{2})}^2+1)({(\sqrt{2})}^2-1)}=
=\frac{{(\sqrt{2})}^2-1}{\sqrt{2}-1}=
=\frac{({(\sqrt{2})}^2-1)(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}=
=\frac{({(\sqrt{2})}^2-1)(\sqrt{2}+1)}{2-1}=
=({(\sqrt{2})}^2-1)(\sqrt{2}+1)=
=(\sqrt[4]{2}-1)(\sqrt{2}+1)