Question

Add and subtract radical's practice

Answer 1

Certainly! Here are some practice problems involving the addition and subtraction of radicals, along with their solutions:

### Practice Problems:

1. **Addition**: \( \sqrt{18} + \sqrt{2} \)

2. **Subtraction**: \( 3\sqrt{5} - 2\sqrt{5} \)

3. **Addition**: \( 4\sqrt{3} + 5\sqrt{3} \)

4. **Subtraction**: \( \sqrt{32} - \sqrt{18} \)

5. **Addition**: \( \sqrt{50} + \sqrt{8} \)

6. **Subtraction**: \( 6\sqrt{2} - 3\sqrt{8} \)

### Solutions:

1. **Solution to \( \sqrt{18} + \sqrt{2} \)**:
- Simplify \( \sqrt{18} \) to \( 3\sqrt{2} \) (since \( \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \)).
- Combine:
\[
3\sqrt{2} + \sqrt{2} = 4\sqrt{2}
\]

2. **Solution to \( 3\sqrt{5} - 2\sqrt{5} \)**:
- Combine like terms:
\[
(3 - 2)\sqrt{5} = 1\sqrt{5} = \sqrt{5}
\]

3. **Solution to \( 4\sqrt{3} + 5\sqrt{3} \)**:
- Combine like terms:
\[
(4 + 5)\sqrt{3} = 9\sqrt{3}
\]

4. **Solution to \( \sqrt{32} - \sqrt{18} \)**:
- Simplify \( \sqrt{32} = 4\sqrt{2} \) and \( \sqrt{18} = 3\sqrt{2} \):
- Combine:
\[
4\sqrt{2} - 3\sqrt{2} = 1\sqrt{2} = \sqrt{2}
\]

5. **Solution to \( \sqrt{50} + \sqrt{8} \)**:
- Simplify \( \sqrt{50} = 5\sqrt{2} \) and \( \sqrt{8} = 2\sqrt{2} \):
- Combine:
\[
5\sqrt{2} + 2\sqrt{2} = 7\sqrt{2}
\]

6. **Solution to \( 6\sqrt{2} - 3\sqrt{8} \)**:
- Simplify \( \sqrt{8} = 2\sqrt{2} \):
- Rewrite and combine:
\[
6\sqrt{2} - 3(2\sqrt{2}) = 6\sqrt{2} - 6\sqrt{2} = 0
\]

### Summary of Answers:
1. \( 4\sqrt{2} \)
2. \( \sqrt{5} \)
3. \( 9\sqrt{3} \)
4. \( \sqrt{2} \)
5. \( 7\sqrt{2} \)
6. \( 0 \)

Feel free to ask for more practice problems or explanations!