6.4-6.7 Review (Algebra 2)

6.4-6.7 Review (Algebra 2)

You can use this as study material for the upcoming assessment!

Topics

• 6.4 Nth Roots

• 6.5 Simplifying More Roots

• 6.6 Rational Exponents

• 6.7 Radical Equations/Inequalities

6.4/6.5 Questions

These are all about simplifying and working with roots!

Multiple Choice

 $\ ^4\sqrt{81x^8}=$  

•  $9x^2$  

•  $3x^2$  

•  $3x^4$  

•  $9x^4$  

Multiple Choice

 $\ ^3\sqrt{64x^7y^3z}=$  

•  $8xy\ \ \sqrt{z}$  

•  $8x^2y\ \ ^3\sqrt{xz}$  

•  $4x^2y\ \sqrt{xz}$  

•  $4x^2y\ \ \ ^3\sqrt{xz}$  

Multiple Choice

 $2\sqrt{48}-\sqrt{75}-\sqrt{12}=$  

•  $\sqrt{3}$  

•  $-\sqrt{3}$  

•  $4\sqrt{3}$  

•  $-3\sqrt{3}$  

Multiple Choice

 $\frac{3+\sqrt{x}}{2-\sqrt{x}}=$  

•  $\frac{6}{4-x}$  

• 6

•  $\frac{6+5x}{4-x}$  

•  $\frac{6+5\sqrt{x}+x}{4-x}$  

Multiple Choice

 $\ ^3\sqrt{2a^2b^7}\cdot\ ^3\sqrt{8ab}\cdot\ ^3\sqrt{8a^3b}\ =$  

•  $8a^2b^3$  

•  $4a^2b^3\ \ ^{\ 3}\sqrt{2}$  

•  $4ab^3\ \ ^3\sqrt{2}$  

6.6 Questions

These are about fraction exponents!

Multiple Choice

 $5^{\frac{2}{5}}=$  

•  $25$  

•  $\ ^5\sqrt{25}$  

•  $125$  

Multiple Choice

 $243^{\frac{3}{5}}=$  

• 27

• 3

• 81

Multiple Choice

 $m^{\frac{3}{4}}\cdot m^{\frac{1}{5}}=$  

•  $m^{\frac{3}{20}}$  

•  $m^{\frac{4}{9}}$  

•  $m^{\frac{19}{20}}$  

Multiple Choice

 $\left(x^2\right)^{\frac{2}{3}}=$  

•  $x^{\frac{2}{3}}$  

•  $x^{\frac{4}{3}}$  

•  $x^{\frac{8}{3}}$  

6.7 Questions

These cover radical equations/inequalities!

Multiple Choice

Solve $\sqrt{2x-2}+4=6$  .

• No Solution

•  $x=3$  

•  $x=6$  

Multiple Choice

Solve $\sqrt{6x-1}=\sqrt{7x+2}$ . 

• No Real Solution

•  $x=-3$  

•  $x=-19$  

Multiple Choice

Solve $5+\sqrt{c-3}\le6$ . 

•  $c\ge3$  

•  $c\le4$  

•  $3\le c\le4$  

That's all!

• Feel free to review this for studying.

• Thanks for working hard!