1. The problem is to find the value of $y$ in the equation $9^2 + 5^2 = y^2$. 2. This is a Pythagorean theorem problem where $a^2 + b^2 = c^2$ for a right triangle. 3. Calculate $9^2 = 81$ and $5^2 = 25$. 4. Substitute these values into the equation: $81 + 25 = y^2$. 5. Simplify the left side: $106 = y^2$. 6. To find $y$, take the square root of both sides: $y = \sqrt{106}$. 7. The exact value of $y$ is $\sqrt{106}$, which is approximately $10.295$. 8. Therefore, $y = \sqrt{106}$ is the solution.