Of the strategies listed, which is most appropriate for solving \( 2(w+1)^{2}=16 ? \) square root property quadratic formula completing the square Correct After isolating the expression that contains the variable, you can use the square ro \[ \begin{array}{l} 2(w+1)^{2}=16 \\ (w+1)^{2}=8 \end{array} \] What are the solutions? Simplify the radical. Enter your answers in the boxes. The solutions are \( \square \) 8 \( \pm \mid 2 \sqrt{2} \)

Let’s dive into the solutions! After your work, we have \((w+1)^{2} = 8\). By applying the square root property, we take the square root of both sides to get: \[ w + 1 = \pm \sqrt{8} = \pm 2\sqrt{2} \] Now, solving for \(w\) gives us: \[ w = -1 \pm 2\sqrt{2} \] Hence, the solutions are: \( w = -1 + 2\sqrt{2} \) and \( w = -1 - 2\sqrt{2} \). Squaring and working with radicals can trip you up! Always remember to check your work by plugging your solutions back into the original equation. It’s like a double check on your homework—proof that you’ve got it right! That way, you can catch any sneaky mistakes. If you're fascinated by solving equations and want to deepen your understanding, check out algebra books or online resources that focus on equations and inequalities. Websites with interactive problem-solving can also be helpful. You might find it fun to tackle more challenging equations and see how the strategies evolve!