1. **State the problem:** Find the modulus of the complex number $z = 3 + i$. 2. **Formula:** The modulus of a complex number $z = a + bi$ is given by $$|z| = \sqrt{a^2 + b^2}$$ where $a$ is the real part and $b$ is the imaginary part. 3. **Identify parts:** Here, $a = 3$ and $b = 1$. 4. **Calculate:** Substitute values into the formula: $$|z| = \sqrt{3^2 + 1^2} = \sqrt{9 + 1} = \sqrt{10}$$ 5. **Final answer:** The modulus of $z = 3 + i$ is $$\boxed{\sqrt{10}}$$.