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!