Honors Algebra 2: Extra Practice on Solving Radical Equations

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

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Solve the following over the real numbers:

1. $$\displaystyle \sqrt[3]{3y^{-1}} = -6$$
2. Solution

$$\displaystyle y = -\frac{1}{72}$$

3. $$\displaystyle 4 - \sqrt{10 - 3a} = a$$
4. Solution

$$\displaystyle a = \{ 2, 3 \}$$

5. $$\displaystyle 3\sqrt{2n + 3} = 2n + 5$$
6. Solution

$$\displaystyle n = \left\{ -1, \frac{1}{2} \right\}$$

7. $$\displaystyle \sqrt{x^{2} + x - 3} = 3$$
8. Solution

$$\displaystyle x = \{-4, 3 \}$$

9. $$\displaystyle \sqrt[3]{y^{2} - 12y} = 4$$
10. Solution

$$\displaystyle y = \{ -4, 16 \}$$

11. $$\displaystyle \sqrt[4]{5x^{2} + 3} = 2 \sqrt[4]{x}$$
12. Solution

$$\displaystyle x = \left\{ \frac{1}{5}, 3 \right\}$$

13. $$\displaystyle \sqrt {\frac{x - 3}{x + 2}} = \frac{2}{3}$$
14. Solution

$$\displaystyle x = 7$$

15. $$\displaystyle \sqrt{\frac{2}{y + 3}} = \sqrt{\frac{3}{2y + 2}}$$
16. Solution

$$\displaystyle y = 5$$

17. $$\displaystyle \sqrt{\frac{x - 2}{x - 2}} = \frac{x - 4}{\sqrt{x - 2}}$$
18. Solution

$$\displaystyle x = 6$$

19. $$\displaystyle \sqrt{y + 15} - \sqrt{2y + 7} = 1$$
20. Solution

$$\displaystyle y = 1$$

21. $$\displaystyle \sqrt{3x - 5} + \sqrt{x - 1} = 2$$
22. Solution

$$\displaystyle x = 2$$

23. $$\displaystyle \sqrt{3x + 9} - \sqrt{2x + 7} = 1$$
24. Solution

$$\displaystyle y = 9$$