Solving Rational / Radical Equations

Rational Equations #1

100

The solution(s) of: (3x-5)^1/4+3=4 

What is: x = 2

200

The solution(s) of: (2x-5)^1/3=3 

What is: x = 16

300

A number that is obtained by solving an equation correctly, but is not actually a solution.

What is an extraneous solution?

400

The solution(s) of: (2x-8)^2/3 = 4 

What are: x = 8 and x = 0

500

The solution(s) of: (6x-3)^2/3 + 6 = 15 

What are: x = 5 and x = -4

Radical Equations #1

100

The solution(s) of: √(5x+6) = x

What is: x=6

200

The solution(s) of: √(4x-3)=5

What is: x = 7

300

√(-3x+10) - √(-7x+38) = 0

x = 7

400

The solution(s) of: √(12x-47) - √(2x+23)=0

What is: x = 7

500

The solution(s) of: √(-9x-14)=0

What is: -14/9

Radical Equations #2

100

The solution(s) of: 2(x - 3)^1/2 + 1 = 7

What is: x = 12

200

The solution(s) of: (7x -12)^1/2 = x 

What is: x = 4 and x = 3

300

Why can you not take the second root of a negative number?

There is no real solution. 

OR

The imaginary number i is defined as the square root of -1.

400

The solution(s) of: -2(x + 4)^1/2  + 5= -7

What is: x = 32

500

The solution(s) of: (x² + 5x + 12)^1/3 = 2

What are: x = -4 and x = -1

Radical Equations #3

100

The solution(s) of: 0.5(x + 2)^1/2 = 1

What is: x = 2

200

The solution(s) of: (x + 3)^1/2 = 2

What are: x = 1

300

What is the fifth root of -32?

-2

400

The solution(s) of: (2x - 1)^1/2 = x

What are: x = 1

500

The solution(s) of: (5x^2 + 14x)^1/3 = x

What are: x = 7, x = -2, and x = 0

Rational Exponent Equations #3

100

The solution(s) of: x^3/2 = 8

What is: x = 4

200

The solution(s) of: x² - 3x - 1 = 0

What are: x = (-3/2) ± (√(29)/2)

300

1) ³√(8))² = 2² = 4  || ³√(8²) = ³√(64) = 4

What are two ways to simplify: 8^2/3

400

The solution(s) of: x^4/3 - 13x^2/3 + 36 = 0

What are: x = ±27, x = ±8

500

The solution(s) of: x^7/6 - 16x^1/2 + 3x^2/3 - 48 = 0

What are: x = 9 (extraneous); x = 64