Solving Radicals & Rational Exponents Review

Determine the solution set of x. Identify any extraneous solutions.

 $\sqrt{x-2}=8$  

•  $x=18$  

•  $x=66$  

•  $x=100$  

•  $x=36$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Determine the solution set of x. Identify any extraneous solutions.

 $\sqrt{5x-3}=\sqrt{2x+6}$  

•  $x=3$  

•  $x=\frac{3}{7}$  

•  $x=\frac{9}{7}$  

•  $x=1$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Determine the solution set of x. Identify any extraneous solutions.

 $\sqrt{x+12}-9=-6$  

•  $x=-3$  

•  $x=18$  

•  $x=-6$  

•  $x=21$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Determine the solution set of x. Identify any extraneous solutions.

 $\sqrt{2x+5}+4=7$  

•  $x=2$  

•  $x=58$  

•  $x=7$  

•  $x=63$  

Tags

CCSS.HSA.REI.A.2

Determine the solution set of x. Identify any extraneous solutions.

 $\sqrt{20-2x}=x+2$  

•  $x=-4$  

  4 is extraneous 

•  $x=4$  

  -4 is extraneous

•  $x=2$  

  -8 is extraneous 

•  $x=-8$  

  2 is extraneous 

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Determine the solution set of x. Identify any extraneous solutions.

 $\sqrt{x-4}+6=x$ 

•  $x=8$  

  4 is extraneous 

•  $x=4$  

  8 is extraneous 

•  $x=5$  

  8 is extraneous 

•  $x=8$  

  5 is extraneous 

Tags

CCSS.HSA.REI.A.2

Determine the solution set of x. Identify any extraneous solutions.

 $\sqrt{4x}=x-3$ 

•  $x=1$  

  9 is extraneous

•  $x=9$  

  1 is extraneous

•  $x=3$  

  -2 is extraneous 
  

•  $x=-2$  

  3 is extraneous 
  

Tags

CCSS.HSA.REI.A.2

On Desmos, graph to solve the following equation for x:

 $\sqrt{2x+5}=\left|x-2\right|+3$  

•  $x=4.828$  

•  $x=2$  

•  $x=3$  

•  $No\ Solution$  

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.D.11

 $\frac{2}{5}\sqrt{4x-5}=2$  

Solve for x.

•  $x=1.25$  

•  $x=3.75$  

•  $x=7.5$  

•  $x=2.5$  

Tags

CCSS.HSA.REI.A.2

Rewrite in radical form.

 $\left(n^2\right)^{\frac{2}{3}}$  

•  $\ ^4\sqrt{n^3}$  

•  $\ ^3\sqrt{n^4}$  

•  $\ ^3\sqrt{n}$  

•  $\sqrt{n^3}$  

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2