Training Radicals & Rational Exponents Placement Test Practice — Radicals
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Placement Test Practice — Radicals

25 min Radicals & Rational Exponents

Placement Test Practice — Radicals & Rational Exponents

This lesson is a practice test covering all the radical and rational-exponent topics from this module. Use it to gauge your readiness and identify areas that need further review.

The problems range from straightforward simplification to multi-step radical equations, mirroring the style and difficulty you would encounter on a placement test.

These problems are modeled after questions you will see on a college math placement test. Work through them without a calculator, then check your answers.

Practice Test — 25 Questions

1. Simplify $\sqrt{108}$
2. Simplify $\sqrt{50} + \sqrt{32}$
3. Evaluate $16^{3/4}$
4. Rationalize $\dfrac{6}{\sqrt{3}}$
5. Simplify $\sqrt{45x^2y^4}$
6. Solve $\sqrt{x + 5} = 3$
7. Evaluate $81^{-3/4}$
8. Simplify $\dfrac{\sqrt{18}}{\sqrt{2}}$
9. Multiply $(\sqrt{7} - 2)(\sqrt{7} + 2)$
10. Solve $\sqrt{4x - 3} = x$
11. Simplify $x^{2/5} \cdot x^{3/5}$
12. Rationalize $\dfrac{5}{\sqrt{7} - \sqrt{2}}$
13. Evaluate $\left(\dfrac{1}{4}\right)^{-3/2}$
14. Simplify $3\sqrt{28} - 2\sqrt{63}$
15. Solve $\sqrt{2x + 5} = x + 1$
16. Express $\sqrt[3]{x^5}$ using rational exponents
17. Evaluate $\sqrt[3]{-64}$
18. Simplify $\sqrt{12} \cdot \sqrt{27}$
19. Simplify $\dfrac{a^{7/3}}{a^{2/3}}$
20. Solve $2\sqrt{x-1} = 6$
21. Simplify $(9x^4)^{1/2}$
22. Rationalize $\dfrac{\sqrt{5}}{\sqrt{5} + 1}$
23. Evaluate $\left(\dfrac{27}{8}\right)^{-2/3}$
24. Simplify $5\sqrt{48} - 2\sqrt{75} + \sqrt{12}$
25. Solve $\sqrt{x + 2} + \sqrt{x} = 2$
Show Answer Key

1. $6\sqrt{3}$

2. $5\sqrt{2} + 4\sqrt{2} = 9\sqrt{2}$

3. $(\sqrt[4]{16})^3 = 2^3 = 8$

4. $2\sqrt{3}$

5. $3xy^2\sqrt{5}$

6. $x = 4$

7. $\dfrac{1}{27}$

8. $\sqrt{9} = 3$

9. $7 - 4 = 3$

10. $x = 3$ ($x=\frac{1}{4}$ is extraneous)

11. $x^1 = x$

12. $\dfrac{5(\sqrt{7}+\sqrt{2})}{5} = \sqrt{7} + \sqrt{2}$

13. $4^{3/2} = 8$

14. $6\sqrt{7} - 6\sqrt{7} = 0$

15. $x = 2$ ($x = -2$ is extraneous)

16. $x^{5/3}$

17. $-4$

18. $\sqrt{324} = 18$

19. $a^{5/3}$

20. $x = 10$

21. $3x^2$

22. $\dfrac{5 - \sqrt{5}}{4}$

23. $\dfrac{4}{9}$

24. $20\sqrt{3} - 10\sqrt{3} + 2\sqrt{3} = 12\sqrt{3}$

25. $x = \dfrac{1}{4}$

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