The problem asks us to solve the equation $(z+9)^2 = 3$ for $z$ using the square root property. We need to express the answer in a simplified form, using radicals if necessary.

1. Problem Description

The problem asks us to solve the equation $(z+9)^2 = 3$ for $z$ using the square root property. We need to express the answer in a simplified form, using radicals if necessary.

2. Solution Steps

First, take the square root of both sides of the equation $(z+9)^2 = 3$:

$\sqrt{(z+9)^2} = \pm\sqrt{3}$

$z+9 = \pm\sqrt{3}$

Now, isolate $z$ by subtracting 9 from both sides:

$z = -9 \pm\sqrt{3}$

Therefore, the two solutions are $z = -9 + \sqrt{3}$ and $z = -9 - \sqrt{3}$.

3. Final Answer

$z = -9 + \sqrt{3}, -9 - \sqrt{3}$