CLEP College Algebra Practice Questions - 3

1. The reduced form of $\sqrt{162x^{11}y^{17}}$ is:
   
   
   1. $18x^{5}y^{8}\sqrt{2xy}$
   2. $9x^{5}y^{8}\sqrt{2}$
   3. $3x^{5}y^{8}\sqrt{2xy}$
   4. $9x^{4}y^{4}\sqrt{2xy}$
   5. $9x^{5}y^{8}\sqrt{2xy}$
   
   
2. $\frac{2\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}$ is equal to:
   
   
   1. $-2$
   2. $1$
   3. $\frac{2x-y}{x-y}$
   4. $\frac{2x-\sqrt{xy}+y}{x-y}$
   5. $\frac{2x-3\sqrt{xy}+y}{x-y}$
   
   
3. Solve the equation: $2x^{6}+52x^{3}-54=0$
   
   
   1. $-27$, $1$
   2. $+3$, $-1$
   3. $-3$
   4. $1$, $27$
   5. $-3$
   
   
4. The reduced form of $\frac{\frac{1}{x+y}-\frac{1}{y}}{x}$ is
   
   
   1. $0$
   2. $1$
   3. $\frac{1}{xy+y^{2}}$
   4. $-\frac{1}{xy+y^{2}}$
   5. $xy+y^{2}$
   
   
5. Solve the equation: $\frac{1}{x-2}+\frac{1}{x+2}=\frac{1}{x^{2}-4}$
   
   
   1. $-\frac{1}{2}$
   2. $\frac{1}{2}$
   3. $\frac{1}{4}$
   4. $2$
   5. $1$
   
   
6. Which factors $5x^{3}-3x^{2}-20x+12$ completely?
   
   
   1. $(5x+3)(x+2)^{2}$
   2. $(5x-3)(x+4)(x-1)$
   3. $(5x+3)(x^{2}-4)$
   4. $(5x^{2}+3)(x-4)$
   5. $(5x-3)(x^{2}+4)$
   
   
7. Reduced $(\frac{7a^{-5}}{5c^{\frac{1}{2}}})^{-1}$
   
   
   1. $\sqrt{\frac{7a^{5}}{5c}}$
   2. $\frac{-14a^{5}}{5c}$
   3. $\frac{7a^{5}\sqrt{c}}{5}$
   4. $\frac{5a^{5}}{7\sqrt{c}}$
   5. $\frac{5}{7}a^{5}\sqrt{c}$