# 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 $$i$$?

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