Let's solve the equations using the Square Root Property.

Problem 5: $(x + 8)^2 = 52$

1. Start by taking the square root of both sides: $\sqrt{(x + 8)^2} = \pm \sqrt{52}$ Simplifying, we get: $x + 8 = \pm \sqrt{52}$

2. Simplify $\sqrt{52}$: $\sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13}$ So the equation becomes: $x + 8 = \pm 2\sqrt{13}$

3. Isolate $x$ by subtracting 8 from both sides: $x = -8 \pm 2\sqrt{13}$

So the solutions are: $x = -8 + 2\sqrt{13} \quad \text{or} \quad x = -8 - 2\sqrt{13}$

Problem 6: $(2x - 3)^2 + 4 = 29$

1. Start by isolating the squared term: $(2x - 3)^2 = 29 - 4$ Simplifying, we get: $(2x - 3)^2 = 25$

2. Take the square root of both sides: $\sqrt{(2x - 3)^2} = \pm \sqrt{25}$ Simplifying, we get: $2x - 3 = \pm 5$

3. Solve for $x$ by considering the two possible cases:

   • Case 1: $2x - 3 = 5$ $2x = 8 \quad \Rightarrow \quad x = 4$
   • Case 2: $2x - 3 = -5$ $2x = -2 \quad \Rightarrow \quad x = -1$

So the solutions are: $x = 4 \quad \text{or} \quad x = -1$

Would you like more details on any of these steps, or do you have any questions?

Related Questions:

1. What is the Square Root Property and how does it work?
2. Can you solve $(x - 7)^2 = 81$ using the Square Root Property?
3. How can you simplify square roots like $\sqrt{52}$ step-by-step?
4. What are some common mistakes to avoid when using the Square Root Property?
5. Can you apply the Square Root Property to solve $(3x + 2)^2 = 36$?

Tip: When using the Square Root Property, always remember to consider both the positive and negative roots.