# Honors Algebra 2: Extra Practice on Simplifying Radicals

• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown

Calculator Inactive.

1. $$\displaystyle \sqrt[4]{48}$$
2. Solution

$$\displaystyle 2\sqrt[4]{3}$$

3. $$\displaystyle \sqrt{75x^3}$$
4. Solution

$$\displaystyle 5x\sqrt{3x}$$

5. $$\displaystyle \sqrt[4]{\left(5x\right)^4}$$
6. Solution

$$\displaystyle 5|x|$$

7. $$\displaystyle \sqrt[3]{24}$$
8. Solution

$$\displaystyle 2\sqrt[3]{3}$$

9. $$\displaystyle \sqrt[3]{24a^4}$$
10. Solution

$$\displaystyle 2a\sqrt[3]{3a}$$

11. $$\displaystyle \sqrt[3]{-40x^6}$$
12. Solution

$$\displaystyle -2x^2 \sqrt[3]{5}$$

13. $$\displaystyle \frac{\sqrt{8}}{2}$$
14. Solution

$$\displaystyle \sqrt{2}$$

15. $$\displaystyle \frac{\sqrt{5} + \sqrt{3}}{\sqrt{3}}$$
16. Solution

$$\displaystyle \frac{\sqrt{15} + 3}{3}$$

17. $$\displaystyle \frac{\sqrt{12} - 3}{\sqrt{8}}$$
18. Solution

$$\displaystyle \frac{2\sqrt{6} - 3\sqrt{2}}{4}$$

19. $$\displaystyle \sqrt{\sqrt[4]{2x}}$$
20. Solution

$$\displaystyle \sqrt[8]{2x}$$

21. $$\displaystyle \sqrt[5]{\sqrt[3]{10a^8b^{15}}}$$
22. Solution

$$\displaystyle b\sqrt[15]{10a^8}$$

23. $$\displaystyle \sqrt[3]{\frac{5}{4y^2}}$$
24. Solution

$$\displaystyle \frac{\sqrt[3]{10y}}{2y}$$

25. $$\displaystyle \frac{6a^2}{\sqrt[4]{8a^2}}$$
26. Solution

$$\displaystyle 3|a|\sqrt[4]{2a^2}$$

27. $$\displaystyle \frac{12n}{\sqrt[3]{9n^7}}$$
28. Solution

$$\displaystyle \frac{4\sqrt[3]{3n^2}}{n^2}$$

29. $$\displaystyle \frac{4}{\sqrt[3]{7} - \sqrt[3]{5}}$$
30. Solution

$$\displaystyle 2\sqrt[3]{49} + 2\sqrt[3]{35} + 2\sqrt[3]{25}$$

31. $$\displaystyle \frac{-2}{\sqrt[3]{a} + 4}$$
32. Solution

$$\displaystyle \frac{-2\sqrt[3]{a^2} + 8\sqrt[3]{a} - 32}{a + 64}$$

33. $$\displaystyle \sqrt[3]{x^{6n}}$$
34. Solution

$$\displaystyle x^{2n}$$

35. $$\displaystyle \sqrt[4]{y^{4n + 12}}$$
36. Solution

$$\displaystyle \left| y^{n + 3}\right|$$

37. $$\displaystyle \sqrt[3]{x^{2n + 1}} \cdot \sqrt[3]{x^{4n + 2}}$$
38. Solution

$$\displaystyle x^{2n + 1}$$

39. $$\displaystyle y^n \cdot \sqrt[4]{y^{3n}} + \sqrt[4]{y^{7n}}, y > 0.$$
40. Solution

$$\displaystyle 2y^n\sqrt[4]{y^{3n}}$$

41. $$\displaystyle \sqrt[n]{x^n}$$
42. Solution

$$x$$ if $$n$$ is odd; $$|x|$$ if $$n$$ is even

43. $$\displaystyle \sqrt[n]{3^{3n + 2}}$$
44. Solution

$$\displaystyle 27 \sqrt[n]{9}$$

45. $$\displaystyle \sqrt[n]{a^nx^{5n+1}}$$ for $$a, x > 0$$
46. Solution

$$\displaystyle ax^5 \sqrt[n]{x}$$ for $$a, x > 0$$

47. $$\displaystyle \sqrt[n]{ab^{2n}x^{2n+3}}$$ for $$a, x > 0$$
48. Solution

$$\displaystyle b^2x^2\sqrt[n]{ax^3}$$ for $$a, x > 0$$