1. **State the problem:** Simplify the expression $$\sqrt[4]{x-6} + \sqrt{x^2+36}$$ and analyze its domain. 2. **Analyze each term:** - The first term is the fourth root $$\sqrt[4]{x-6}$$, which requires $$x-6 \geq 0$$ to be real. So, $$x \geq 6$$. - The second term $$\sqrt{x^2+36}$$ is a square root of a sum of a square and a positive number, so it's always real and $$\geq 6$$. 3. **Domain:** - The entire expression is defined for $$x \geq 6$$ only because of the first term. 4. **Simplification:** - The expression cannot be simplified algebraically further because the two radicals have different roots and different radicands. 5. **Final answer:** - Expression: $$\sqrt[4]{x-6} + \sqrt{x^2+36}$$ - Domain: $$x \geq 6$$ where the expression is real-valued.