https://file.aiquickdraw.com/mathbot/file/17266411155572syozizv.jpg

Let's solve each of the problems step by step.

### 1. \( 3\sqrt{7} + \sqrt{700} - \sqrt{28} \)

- Simplify the square roots:
  \[
  \sqrt{700} = \sqrt{100 \times 7} = 10\sqrt{7}, \quad \sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}
  \]
- Substitute and combine like terms:
  \[
  3\sqrt{7} + 10\sqrt{7} - 2\sqrt{7} = (3 + 10 - 2)\sqrt{7} = 11\sqrt{7}
  \]
- **Answer: \( 11\sqrt{7} \)**

---

### 2. \( \sqrt{125} + \sqrt{720} - 9\sqrt{5} \)

- Simplify the square roots:
  \[
  \sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}, \quad \sqrt{720} = \sqrt{144 \times 5} = 12\sqrt{5}
  \]
- Substitute and combine like terms:
  \[
  5\sqrt{5} + 12\sqrt{5} - 9\sqrt{5} = (5 + 12 - 9)\sqrt{5} = 8\sqrt{5}
  \]
- **Answer: \( 8\sqrt{5} \)**

---

### 3. \( \sqrt{400} + \sqrt{125} + \sqrt{500} \)

- Simplify the square roots:
  \[
  \sqrt{400} = 20, \quad \sqrt{125} = 5\sqrt{5}, \quad \sqrt{500} = \sqrt{100 \times 5} = 10\sqrt{5}
  \]
- Combine like terms:
  \[
  20 + 5\sqrt{5} + 10\sqrt{5} = 20 + 15\sqrt{5}
  \]
- **Answer: \( 20 + 15\sqrt{5} \)**

---

### 4. \( \sqrt{48} - \sqrt{768} + 7\sqrt{3} \)

- Simplify the square roots:
  \[
  \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}, \quad \sqrt{768} = \sqrt{256 \times 3} = 16\sqrt{3}
  \]
- Substitute and combine like terms:
  \[
  4\sqrt{3} - 16\sqrt{3} + 7\sqrt{3} = (4 - 16 + 7)\sqrt{3} = -5\sqrt{3}
  \]
- **Answer: \( -5\sqrt{3} \)**

---

### 5. \( 9\sqrt{2} - \sqrt{578} + \sqrt{72} \)

- Simplify the square roots:
  \[
  \sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}, \quad \sqrt{578} \text{ is not a simple square root}.
  \]
- Approximate \( \sqrt{578} \approx 24.04 \), and simplify the expression:
  \[
  9\sqrt{2} + 6\sqrt{2} - 24.04 = 15\sqrt{2} - 24.04
  \]
- **Answer: \( 15\sqrt{2} - 24.04 \)**

---

Would you like more details or have any questions about these solutions?

Here are 5 related questions:
1. How do you simplify square roots of non-perfect squares?
2. Can you explain how to combine like terms in radical expressions?
3. How do you approximate square roots without a calculator?
4. How does factoring help in simplifying square roots?
5. What are some common square root simplifications?

**Tip:** Always look for factors of the radicand (the number under the square root) that are perfect squares to simplify square roots efficiently!

Solve the following radical expressions:
1. 3√7 + √700 - √28
2. √125 + √720 - 9√5
3. √400 + √125 + √500
4. √48 - √768 + 7√3
5. 9√2 - √578 + √72

Step-by-step solutions to radical expression problems, including √700, √125, √578, and more. Learn how to simplify square roots and combine like terms with radicals, perfect for Grades 9-12 students.

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