This worksheet provides ten practice problems for solving quadratic equations using the square root property method.

Problem: Solve each quadratic equation using the Square Root Property.

The square root property states that if \( x^2 = k \), then:
\[
x = \pm \sqrt{k}
\]
This means we take both the positive and negative square roots of \( k \).

Let's solve each equation step by step.

---

#### 1) \( n^2 - 12 = 0 \)

1. Add 12 to both sides:
\[
n^2 = 12
\]

2. Apply the square root property:
\[
n = \pm \sqrt{12}
\]

3. Simplify \( \sqrt{12} \):
\[
\sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3}
\]

4. Solution:
\[
n = \pm 2\sqrt{3}
\]

---

#### 2) \( p^2 = -36 \)

1. Notice that \( p^2 = -36 \). Since the square of any real number is non-negative, there are no real solutions for this equation.

2. Solution:
\[
\text{No real solutions}
\]

---

#### 3) \( (k - 6)^2 = 49 \)

1. Apply the square root property:
\[
k - 6 = \pm \sqrt{49}
\]

2. Simplify \( \sqrt{49} \):
\[
\sqrt{49} = 7
\]

3. So:
\[
k - 6 = 7 \quad \text{or} \quad k - 6 = -7
\]

4. Solve for \( k \):
\[
k = 7 + 6 = 13 \quad \text{or} \quad k = -7 + 6 = -1
\]

5. Solution:
\[
k = 13 \quad \text{or} \quad k = -1
\]

---

#### 4) \( r^2 - 32 = 0 \)

1. Add 32 to both sides:
\[
r^2 = 32
\]

2. Apply the square root property:
\[
r = \pm \sqrt{32}
\]

3. Simplify \( \sqrt{32} \):
\[
\sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}
\]

4. Solution:
\[
r = \pm 4\sqrt{2}
\]

---

#### 5) \( u^2 = 64 \)

1. Apply the square root property:
\[
u = \pm \sqrt{64}
\]

2. Simplify \( \sqrt{64} \):
\[
\sqrt{64} = 8
\]

3. Solution:
\[
u = \pm 8
\]

---

#### 6) \( (h + 1)^2 = 16 \)

1. Apply the square root property:
\[
h + 1 = \pm \sqrt{16}
\]

2. Simplify \( \sqrt{16} \):
\[
\sqrt{16} = 4
\]

3. So:
\[
h + 1 = 4 \quad \text{or} \quad h + 1 = -4
\]

4. Solve for \( h \):
\[
h = 4 - 1 = 3 \quad \text{or} \quad h = -4 - 1 = -5
\]

5. Solution:
\[
h = 3 \quad \text{or} \quad h = -5
\]

---

#### 7) \( (y + 2)^2 = -9 \)

1. Notice that \( (y + 2)^2 = -9 \). Since the square of any real number is non-negative, there are no real solutions for this equation.

2. Solution:
\[
\text{No real solutions}
\]

---

#### 8) \( m^2 + 63 = 0 \)

1. Subtract 63 from both sides:
\[
m^2 = -63
\]

2. Notice that \( m^2 = -63 \). Since the square of any real number is non-negative, there are no real solutions for this equation.

3. Solution:
\[
\text{No real solutions}
\]

---

#### 9) \( w^2 - 72 = 0 \)

1. Add 72 to both sides:
\[
w^2 = 72
\]

2. Apply the square root property:
\[
w = \pm \sqrt{72}
\]

3. Simplify \( \sqrt{72} \):
\[
\sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2}
\]

4. Solution:
\[
w = \pm 6\sqrt{2}
\]

---

#### 10) \( a^2 - 25 = 0 \)

1. Add 25 to both sides:
\[
a^2 = 25
\]

2. Apply the square root property:
\[
a = \pm \sqrt{25}
\]

3. Simplify \( \sqrt{25} \):
\[
\sqrt{25} = 5
\]

4. Solution:
\[
a = \pm 5
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1) & \quad n = \pm 2\sqrt{3} \\
2) & \quad \text{No real solutions} \\
3) & \quad k = 13 \text{ or } k = -1 \\
4) & \quad r = \pm 4\sqrt{2} \\
5) & \quad u = \pm 8 \\
6) & \quad h = 3 \text{ or } h = -5 \\
7) & \quad \text{No real solutions} \\
8) & \quad \text{No real solutions} \\
9) & \quad w = \pm 6\sqrt{2} \\
10) & \quad a = \pm 5
\end{aligned}
}
\]