Unit 2 Review

Unit 2 Review

Radicals

Radical Arithmetic

• Treat like variables (e.g. distribute, combine like terms)

• Simplify Radicands (e.g. factor)

Fill in the Blanks

 $\sqrt{3}\cdot\sqrt{12}$  

Multiple Choice

 $\sqrt{2}\left(3+\sqrt{8}\right)$  

•  $3\sqrt{2}+4$  

•  $3\sqrt{2}+16$  

•  $3\sqrt{2}+\sqrt{16}$  

•  $3\sqrt{2}+3\sqrt{8}$  

Multiple Choice

 $\sqrt{12x^3y}+2\sqrt{27x\cdot y^3}$  

•  $2\left(\sqrt{3x^3y}+\sqrt{27x\cdot y^3}\right)$  

•  $\sqrt{3xy}\left(2x+6y\right)$  

• Can't be simplified

Multiple Choice

What is the simplification mistake?
Step 1:  $\sqrt{72x^5y^2}$  =
Step 2:   $\sqrt{9\cdot8\cdot x^4\cdot x\cdot y^2}$  =
Step 3:   $3x^2y\sqrt{8x}$  

• Between Step 1 & 2... 72 doesn't factor to 9*8

• Between Step 2 & 3...  $x^4$  doesn't simplify to  $x^2$  

• Step 3... 8 can be simplified farther.

Fill in the Blanks

 $\sqrt{x-8}​+5=7$  

Fill in the Blanks

 $2\sqrt{3x+4}+1=5$  

Multiple Choice

What is an extraneous solution?

• An extra solution.

• A solution often from equations with radicals that does not make the original equation true.

• A solution that makes an equation true.

• A solution that results from making a mistake.

Extraneous Solutions

• A number found when solving an equation correctly with algebra that is not a solution!

• Check your answer when solving radicals. If you get something like -3=3 when you check, the solution is extraneous.

Fill in the Blanks

Solve the equation. You should get two solutions. Enter the extraneous solution.

 $\sqrt{3x+4}=x$  

Multiple Select

Select all the equivalent expressions of  $∛8^2$  

• 4

•  $8^{\frac{2}{3}}$  

•  $8^{\frac{3}{2}}$  

•  $∛64$