Rational Exponents and Radical Functions

Simplify Radicals

100

root(3)(8y^9)

2y^3

200

sqrt(16x^2-24x+9)

4x-3

300

 root(8)(v^8g^40) 

pmvg^5

400

root(6)(729a^24b^18

pm3a^4b^3

500

 sqrt(root(5)(32)

sqrt(2)

Properties of Exponents and Radicals

100

  root(3)(4) (6 root(3)(3) -1)

6 root(3)(12)-  root(3)(4) 

200

 root(4)(2) x  root(4)(32) 

2 root(4)(2) 

300

frac{6}{1+sqrt2

-6+6sqrt2

400

 (5sqrt3+6)(5sqrt3-6) 

39

500

sqrt(6x)+sqrt(2x)/sqrt(3)-sqrt(3x)/sqrt(2)

(5sqrt(6x))/6

Graphing Radical Functions

100

What transformation does the following equation have?

 f(x)=root(3)(x-3) 

right 3 units

200

What transformation does the following equation have? f(x)=sqrtx+1 

up one unit

300

What is the domain of 5sqrt(x-7)+2?

x is greater than or equal to 7

400

What is the range of root(3)(x+13)-4

all real numbers

500

Write a square root function that has a domain of x≥4 

sqrt(x-4) with any a and k values

Solving Radical Equations

100

 13-root(4)(x)=10 

81

200

3x^1/3 -2 = -4

-8/27

300

 sqrt(6x-20)-x=6 

4, 14

4 is extraneous

400

 sqrt(5x+1)+1=x 

0, 7

0 is extraneous

500

sqrt(x=8)=sqrt(x)+sqrt(3)

25/12

Complex Numbers

100

Simplify i² 

-1

200

Simplify (3+i)(3-i)

10

300

Simplify 3/(1-2i)

3/5 + 6/5 i

400

Simplify i¹⁷

i

500

What is the absolute value of 5-5i

5sqrt(2)

nth Roots, Radicals, and Rational Exponents

100

Simplify  root(4)(16) 

2, -2

200

What is   81^(1/4) 

3,-3

300

 root(3)(27x^12) 

 3x^(4) 

400

 6y^(3)=750 

5

500

root(6)(8^3)/root(4)(4^2) 

sqrt(2)