1. **State the problem:** We need to find which expression is equivalent to $\sqrt{63}$.\n\n2. **Recall the property of square roots:** For any positive numbers $a$ and $b$, $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ and $\sqrt{a} + \sqrt{b} \neq \sqrt{a + b}$.\n\n3. **Evaluate each option:**\n- Option 1: $\sqrt{36} + \sqrt{27} = 6 + 3\sqrt{3}$ (since $\sqrt{36} = 6$ and $\sqrt{27} = 3\sqrt{3}$). This is not equal to $\sqrt{63}$.\n- Option 2: $\sqrt{9} \cdot \sqrt{7} = \sqrt{9 \cdot 7} = \sqrt{63}$. This matches $\sqrt{63}$.\n- Option 3: $\sqrt{36} \cdot \sqrt{27} = \sqrt{36 \cdot 27} = \sqrt{972}$. This is not equal to $\sqrt{63}$.\n- Option 4: $\sqrt{9} + \sqrt{7} = 3 + \sqrt{7}$. This is not equal to $\sqrt{63}$.\n\n4. **Conclusion:** Only Option 2 is equivalent to $\sqrt{63}$.