1. The problem is to evaluate $\sqrt[4]{9}$, which means finding the fourth root of 9. 2. Recall that the fourth root of a number $a$ is the number $x$ such that $x^4 = a$. 3. We can rewrite 9 as $9 = 3^2$. 4. Therefore, $\sqrt[4]{9} = \sqrt[4]{3^2} = (3^2)^{\frac{1}{4}} = 3^{\frac{2}{4}} = 3^{\frac{1}{2}}$. 5. Now, $3^{\frac{1}{2}}$ is the square root of 3, so $\sqrt[4]{9} = \sqrt{3}$. 6. The simplest exact form is $\sqrt{3}$, which is approximately 1.732. Final answer: $\sqrt[4]{9} = \sqrt{3}$