fbpx
calculus online - Free exercises and solutions to help you succeed!

Powers and Roots – Simplify an expression with roots – Exercise 5679

Exercise

Simplify the expression:

\frac{1}{\sqrt[4]{2}+1}

Final Answer

(\sqrt[4]{2}-1)(\sqrt{2}+1)

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)

Share with Friends

Leave a Reply