Multiplying Radicals Worksheet

Multiplying Radicals

Read each question carefully and show all your work. Simplify all radical expressions to their simplest form. Rationalize all denominators where necessary.

1. Multiply and simplify: \( \sqrt{3} \cdot \sqrt{12} \)

2. Multiply and simplify: \( 2\sqrt{5} \cdot 3\sqrt{10} \)

3. Expand and simplify: \( \sqrt{2}(\sqrt{8} + \sqrt{18}) \) =  

4. Expand and simplify: \( 4\sqrt{3}(2\sqrt{6} - \sqrt{3}) \) =  

5. Multiply and simplify: \( (\sqrt{7} + 2)(\sqrt{7} - 2) \)

6. Multiply and simplify: \( (2\sqrt{3} + 5)( \sqrt{3} - 1) \)

7. Rationalize the denominator and simplify: \( \frac{6}{\sqrt{3}} \)

8. Rationalize the denominator and simplify: \( \frac{1}{2 + \sqrt{5}} \)

9. Simplify completely: \( (\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y}) \)

10. Rationalize the denominator: \( \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} \)