Solve the quadratic equation by the square root method and write the solutions in radical form. Simplify the solutions.
\[
(7 y+7)^{2}=27
\]
Answer

Step 1 ：The given equation is a quadratic equation in the form of \((a+b)^2 = c\). To solve this, we can take the square root of both sides. However, we must remember that when we take the square root of both sides, we get two solutions: one positive and one negative.

Step 2 ：Let's solve the equation \((7y + 7)^2 = 27\).

Step 3 ：Taking the square root of both sides, we get \(7y + 7 = \sqrt{27}\) and \(7y + 7 = -\sqrt{27}\).

Step 4 ：Solving for y, we get \(y = -1 - \frac{3\sqrt{3}}{7}\) and \(y = -1 + \frac{3\sqrt{3}}{7}\).

Step 5 ：Final Answer: \(\boxed{y = -1 - \frac{3\sqrt{3}}{7}, -1 + \frac{3\sqrt{3}}{7}}\)