# The Cube Root of \(i\)?

**Algebra**Level 2

First, you can read about the definition of \(i\), Imaginary Unit in the Brilliant.org Algebra Glossary

Let

\(\sqrt[3]{\strut i}=\displaystyle \frac{\sqrt{a}+i}{b}\)

where \(a\) and \(b\) is positive integers and \(a\) is not a square number.

What is the value of \(a+b\)?

This problem is inspired by The Square Root of \(i\)?