Questions: Solve by using the square root property. Express the solution set in exact simplest form. [ (z+11)^2=28 ] Apply the square root property. Do not simplify the radical. [ z+11=pmsqrt28 ]

Solution Steps

To solve the equation \((z+11)^2 = 28\) using the square root property, we need to take the square root of both sides of the equation. This will give us two possible solutions because the square root of a number can be both positive and negative. After taking the square root, we will isolate \(z\) by subtracting 11 from both sides.

1. Take the square root of both sides of the equation.
2. Isolate \(z\) by subtracting 11 from both sides.

Starting with the equation: \[ (z + 11)^2 = 28 \] we apply the square root property, which gives us: \[ z + 11 = \pm \sqrt{28} \]

Calculating the square root, we find: \[ \sqrt{28} \approx 5.2915 \] Thus, we have two equations: \[ z + 11 = 5.2915 \quad \text{and} \quad z + 11 = -5.2915 \]

Now, we isolate \(z\) in both cases:

1. For the positive case: \[ z = 5.2915 - 11 = -5.7085 \]
2. For the negative case: \[ z = -5.2915 - 11 = -16.2915 \]

Final Answer