Unit 3 Study Guide: Radical Expressions

Unit 3 Study Guide: Radical Expressions

Name: _________________________

Date: __________________________

Part 1: Simplifying Radicals

1. \( \sqrt{48} \)

2. \( \sqrt{150} \)

3. \( \sqrt[3]{40} \)

4. \( 5\sqrt{32} \)

5. \( -2\sqrt[3]{16} \)

Part 2: Operations with Radicals

6. \( 8\sqrt{5} - 3\sqrt{5} \)

7. \( \sqrt{12} + \sqrt{27} \)

8. \( \sqrt{3} \cdot \sqrt{15} \)

9. \( (2\sqrt{6}) \cdot (4\sqrt{3}) \)

10. \( \sqrt{5}(2 + \sqrt{5}) \)

11. \( 4\sqrt{20} - \sqrt{45} \)

Part 3: Radicals & Fractional Exponents

12. Convert to radical form: \( x^{5/2} \)

13. Convert to exponential form: \( \sqrt[4]{y^3} \)

14. Evaluate: \( 16^{3/4} \)

Part 4: Rationalizing the Denominator

15. \( \frac{3}{\sqrt{2}} \)

16. \( \frac{10}{\sqrt{5}} \)

17. \( \sqrt{\frac{5}{3}} \)

18. \( \frac{6}{\sqrt{20}} \)