# Honors Algebra 2: Assignment 43: Unit Review

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

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Simplify Completely. Make sure the domain and range of the simplified version match the domain and range of the original:

1. $$\displaystyle \sqrt[5]{4x^6}$$
2. Solution

$$\displaystyle x \sqrt[5]{4x}$$

3. $$\displaystyle \sqrt{189x^5}$$
4. Solution

$$\displaystyle 3x^2 \sqrt{21x}$$

5. $$\displaystyle \sqrt[4]{\left(-81 \right) ^{-2}}$$
6. Solution

$$\displaystyle \frac{1}{9}$$

7. $$\displaystyle \sqrt[6]{8} \cdot \sqrt[6]{27}$$
8. Solution

$$\displaystyle \sqrt{6}$$

9. $$\displaystyle \frac{5}{\displaystyle \sqrt{10} - \sqrt{15}}$$
10. Solution

$$\displaystyle -\sqrt{10} - \sqrt{15}$$

11. $$\displaystyle \frac{\sqrt{x + y}}{5 - \sqrt{x + y}}$$ given $$x > 0$$ and $$y > 0$$
12. Solution

$$\displaystyle \frac{5\sqrt{x + y} + x + y}{25 - x - y}$$

13. $$\displaystyle \sqrt[4]{\displaystyle \frac{7}{250a^3}}$$ given $$a > 0$$
14. Solution

$$\displaystyle \frac{\sqrt[4]{280a}}{10a}$$

15. $$\displaystyle 5\sqrt{12x} - 6\sqrt{48x} + 75\sqrt{x}$$
16. Solution

$$\displaystyle -14\sqrt{3x} + 75 \sqrt{x}$$

For each of the following, evaluate or identify as undefined:

1. $$\displaystyle \sqrt[3]{-54}$$
2. Solution

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

3. $$\displaystyle \sqrt[5]{(-32)^4}$$
4. Solution

16

5. $$\displaystyle \sqrt{-\frac{1}{8}}$$
6. Solution

undefined

7. $$\displaystyle \sqrt{\frac{1}{8}}$$
8. Solution

$$\displaystyle \frac{\sqrt{2}}{4}$$

Simplify completely. Where appropriate, make sure the domain and range of the simplified version is the same as the original.

1. $$\displaystyle \sqrt{50} + 3\sqrt{18x^2} + x\sqrt{8}$$
2. Solution

$$\displaystyle 5\sqrt{2}+ 2x\sqrt{2} + 9|x|\sqrt{2}$$

3. $$\displaystyle \sqrt[3]{16x^3y^5}$$
4. Solution

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

5. $$\displaystyle \sqrt[4]{\frac{16x^4y^9}{z}}$$
6. Solution

$$\displaystyle \frac{2 \left| x \right| y^2 \sqrt[4]{yz^3}}{\left| z \right|}$$ where $$y$$ and $$z$$ have the same sign.

7. $$\displaystyle \sqrt{48} \cdot \sqrt[6]{216}$$
8. Solution

$$\displaystyle 12\sqrt{2}$$

9. $$\displaystyle \sqrt{27a^2b^4} \cdot \sqrt{3ab^3}$$
10. Solution

$$\displaystyle 9ab^3\sqrt{ab}$$ where $$a$$ and $$b$$ have the same sign.

11. $$\displaystyle \sqrt[3]{\frac{128x^6}{2y^5}}$$
12. Solution

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

13. $$\displaystyle \frac{4}{2 + 2\sqrt{3}}$$
14. Solution

$$\displaystyle \sqrt{3} - 1$$

15. $$\displaystyle \left( 2 - 3\sqrt{5} \right)^2$$
16. Solution

$$\displaystyle 49-12\sqrt{5}$$

17. $$\displaystyle \sqrt{\frac{3}{5}} \left( \frac{\sqrt{5}}{2} + \sqrt{6} \right)$$
18. Solution

$$\displaystyle \frac{\left( 5 \sqrt{3} + 6\sqrt{10}\right)}{10}$$

19. $$\displaystyle \sqrt{4x^{-1} + 4y^{-1}} \cdot \sqrt{ \left( x + y \right) ^{-1}}$$, given $$x > 0$$ and $$y > 0$$
20. Solution

$$\displaystyle \frac{2 \sqrt{xy}}{xy}$$

21. $$\displaystyle \sqrt[3]{16x^4y^7} - xy\sqrt[3]{2xy^4}$$
22. Solution

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

23. $$\displaystyle \sqrt[10]{\frac{1}{32}}$$
24. Solution

$$\displaystyle \frac{\sqrt{2}}{2}$$

Solve the following:

1. $$\displaystyle m + \sqrt{m - 2} - 4 = 0$$
2. Solution

$$\displaystyle \{ 3 \}$$

3. $$\displaystyle \sqrt{m + 10} + \sqrt{2m + 4} - 8 = 0$$
4. Solution

$$\displaystyle \{ 6 \}$$