1. The problem is to simplify the expression $\sqrt{2} (7 + \sqrt{3})$. 2. We use the distributive property: $a(b+c) = ab + ac$. 3. Apply this to the expression: $$\sqrt{2} \times 7 + \sqrt{2} \times \sqrt{3}$$ 4. Simplify each term: - $\sqrt{2} \times 7 = 7\sqrt{2}$ - $\sqrt{2} \times \sqrt{3} = \sqrt{2 \times 3} = \sqrt{6}$ 5. Combine the terms: $$7\sqrt{2} + \sqrt{6}$$ 6. This matches option A. Therefore, the simplified expression is $7\sqrt{2} + \sqrt{6}$.