1. **State the problem:** Simplify the equation $$Y(x) = \sqrt{8x + 10} + 40$$. 2. **Understand the components:** The equation consists of a square root term $$\sqrt{8x + 10}$$ and a constant term 40. 3. **Simplify inside the square root if possible:** Check if the expression inside the square root can be factored or simplified. 4. The expression $$8x + 10$$ can be factored as $$2(4x + 5)$$, but since 2 is not a perfect square, it cannot be simplified further under the square root. 5. **Rewrite the square root using the factorization:** $$\sqrt{8x + 10} = \sqrt{2(4x + 5)} = \sqrt{2} \times \sqrt{4x + 5}$$ 6. **Final simplified form:** $$Y(x) = \sqrt{2} \times \sqrt{4x + 5} + 40$$ This is the simplest exact form unless you want to approximate the square root of 2 numerically.