Review Chapter 6: Irrational and Complex Numbers

Simplify:

 $\sqrt{x^2}$  

• -x

• x

•  $\left|x\right|$  

•  $-\left|x\right|$  

Find the real roots of the equation:

 $2-y^2=0$  

•  $\sqrt{2}$  

•  $\pm i\sqrt{2}$  

•  $\pm\sqrt{2}$  

• no real roots

Simplify:

 $\sqrt{12x^4y^7}$  

Assume that the radical represents a real number.

•  $x^2y^2\sqrt{12y}$  

•  $2x^2y^3\sqrt{3y}$  

•  $6x^2y^3\sqrt{y}$  

•  $x^2\sqrt{12y^7}$  

Simplify:

 $\sqrt{18}\cdot\sqrt{\frac{3}{10}}$  

•  $\frac{3\sqrt{15}}{5}$  

•  $15\sqrt{3}$  

•  $\frac{\sqrt{15}}{5}$  

•  $\frac{3\sqrt{6}}{\sqrt{10}}$  

Simplify:

 $\sqrt{6}\left(\frac{\sqrt{2}}{2}+\sqrt{3}\right)-\sqrt{8}$  

•  $\sqrt{3}+\sqrt{2}$  

•  $\sqrt{3}+5\sqrt{2}$  

•  $\sqrt{5}$  

•  $2\sqrt{3}+\sqrt{2}$  

Simplify:

 $\sqrt{72x^3}-5x\sqrt{2x}$  

Assume that each radical represents a real number.

•  $\sqrt{2x}$  

•  $2x\sqrt{x}$  

•  $x^2\sqrt{2x}$  

•  $x\sqrt{2x}$  

Simplify:

 $\left(2\sqrt{6}-\sqrt{3}\right)^2$  

• 21

•  $27-6\sqrt{2}$  

•  $27-12\sqrt{2}$  

•  $15-12\sqrt{2}$  

Simplify:

 $\frac{6}{3+2\sqrt{3}}$  

•  $6-4\sqrt{3}$  

•  $6+4\sqrt{3}$  

•  $-6+4\sqrt{3}$  

•  $-6-4\sqrt{3}$  

Simplify:

 $^3\sqrt{\frac{\ 5\ }{4}}$  

•  $\frac{^3\sqrt{5}}{^3\sqrt{4}}$  

•  $\frac{^3\sqrt{10}}{2}$  

•  $\frac{^3\sqrt{20}}{2\ ^3\sqrt{2}}$  

•  $^3\sqrt{\frac{\ 5\ }{4}}$  

Solve:

 $3-2\sqrt{x}=7$  

•  $\left\{-2\right\}$  

•  $\left\{4\right\}$  

•  $\left\{-4\right\}$  

• No solution