1. **State the problem:** Calculate the value of $\sqrt{8} + \sqrt{2}$.\n\n2. **Recall the properties of square roots:** The square root of a product can be expressed as the product of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$.\n\n3. **Simplify $\sqrt{8}$:** Since $8 = 4 \times 2$, we have $$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}.$$\n\n4. **Rewrite the expression:** Now the expression becomes $$2\sqrt{2} + \sqrt{2}.$$\n\n5. **Combine like terms:** Both terms have $\sqrt{2}$, so we add the coefficients: $$2\sqrt{2} + 1\sqrt{2} = (2 + 1)\sqrt{2} = 3\sqrt{2}.$$\n\n**Final answer:** $$\sqrt{8} + \sqrt{2} = 3\sqrt{2}.$$