1. The problem asks us to simplify the expression \(4 \sqrt{2}\). 2. Here, \(\sqrt{2}\) is the square root of 2, and the number 4 is multiplied by this square root. 3. Since 4 is outside the square root, the expression is already in its simplest form when written as \(4 \sqrt{2}\). 4. If desired, we can approximate the value by calculating \(\sqrt{2} \approx 1.414\). 5. Multiplying gives \(4 \times 1.414 = 5.656\). 6. Therefore, \(4 \sqrt{2} = 4 \times \sqrt{2} \) (exact form) or approximately 5.656.