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Let's go through the exercises and solve them one by one.

**3) Resuelve aplicando propiedades cuando sea posible:**

### a) \((\sqrt{8} + \sqrt{2})^2\)

Apply the formula \((a + b)^2 = a^2 + 2ab + b^2\):

\[
\sqrt{8} = 2\sqrt{2}
\]

Now we have:

\[
(2\sqrt{2} + \sqrt{2})^2 = \left(3\sqrt{2}\right)^2 = 9 \cdot 2 = 18
\]

**Answer: 18**

---

### b) \(\sqrt{50} =\)

\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}
\]

**Answer: \(5\sqrt{2}\)**

---

### c) \(\sqrt{100} - \sqrt{36} =\)

\[
\sqrt{100} = 10, \quad \sqrt{36} = 6
\]
\[
10 - 6 = 4
\]

**Answer: 4**

---

### d) \((a^3 : a^2) : (a^4 : a)\)

Using properties of exponents:

\[
\frac{a^3}{a^2} = a^{3-2} = a
\]
\[
\frac{a^4}{a} = a^{4-1} = a^3
\]
\[
\frac{a}{a^3} = a^{1-3} = a^{-2} = \frac{1}{a^2}
\]

**Answer: \(\frac{1}{a^2}\)**

---

### e) \(\sqrt{4 \cdot 81 \cdot 64}\)

Simplify the square roots:

\[
\sqrt{4} = 2, \quad \sqrt{81} = 9, \quad \sqrt{64} = 8
\]
\[
2 \cdot 9 \cdot 8 = 144
\]

**Answer: 144**

---

### f) \(3 \cdot \sqrt{12} =\)

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

\[
3 \cdot 2\sqrt{3} = 6\sqrt{3}
\]

**Answer: \(6\sqrt{3}\)**

---

### g) \(\sqrt{36 + 64} =\)

Simplify the addition:

\[
36 + 64 = 100
\]
\[
\sqrt{100} = 10
\]

**Answer: 10**

---

Let me know if you would like further explanations on any of the steps. Here are some related questions:

1. What are the properties of square roots that simplify complex expressions?
2. How do you apply exponent rules when dividing expressions with the same base?
3. Why is \((a + b)^2\) expanded using the distributive property?
4. How can you simplify roots of products of numbers?
5. In which scenarios would negative exponents arise, and how do you interpret them?

**Tip:** When simplifying square roots, always look for perfect squares within the number to make calculations easier.

3) Resuelve aplicando propiedades cuando sea posible:
a) (√8 + √2)^2 =
b) √50 =
c) √100 - √36 =
d) (a^3 : a^2) : (a^4 : a) =
e) √4·81·64 =
f) 3·√12 =
g) √36+64 =

Solve exercises involving square roots, exponent rules, and radical simplification. Learn step-by-step methods for problems like (√8 + √2)^2, √100 - √36, and others. Suitable for students in Grades 9-10.

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