Roots & Radical Expressions

Roots & Radical Expressions

​Dr. Tom Giles

Simplifying Radical Expressions

Multiple Choice

 Write in exponential form
 ∛x⁷

• x⁷∕ ³

• x3⁄7

• 3x⁷

• 7x³

Multiple Choice

Write in exponential form
√x⁵

• X¹∕ ⁵
• X ²⁄⁵
• X⁵⁄ ²
• X⁵

Multiple Choice

Simplify 4^1/3 x 4^4/3

• 4^5/3
• 4
• 2⁵

Multiple Choice

• a
• b
• c
• d

Multiple Choice

(6^3/4)^1/3

• 6^1/4

• 6^3/12

• 6^4/7

• 6^9/12

Multiple Choice

(x^2/3)⁴

• x^8/3

• x^8/12

• x⁸

• x³

Multiple Choice

Simplify.  Your answer should only contain positive exponents.

• A

• B

• C

• D

Multiple Choice

Simplify.  Your answer should only contain positive exponents.

• A

• B

• C

• D

Multiple Choice

Simplify.  Your answer should only contain positive exponents.

• A

• B

• C

• D

Multiple Choice

Simplify.  Your answer should only contain positive exponents.

• A

• B

• C

• D

Multiple Choice

Simplify.  Your answer should only contain positive exponents.

• A

• B

• C

• D

Multiple Choice

Simplify.  Your answer should only contain positive exponents.

• A

• B

• C

• D

Multiple Choice

What is the cube root of 1000?

• 10

• 100

• 500

• 20

Multiple Choice

What is the cube root of 8?

• 4

• 2

• -2

• -4

​Solving Equations

Equations with radicals that have variables in their radicands are called radical equations. An example of a radical equation is 2 √—x + 1 = 4.

​Solving Equations

To solve a radical equation, follow these steps:

Step 1 Isolate the radical on one side of the equation, if necessary.

Step 2 Raise each side of the equation to the same exponent to eliminate the radical and obtain a linear, quadratic, or other polynomial equation.

Step 3 Solve the resulting equation using techniques you learned in previous chapters. Check your solution.

Solving an Equation with an Extraneous Solution

Raising each side of an equation to the same exponent may introduce extraneous solutions. When you use this procedure, you should always check each apparent solution in the original equation.

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• No solution

• 33

• 61

• 47

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• -5

• 5

• 10

• 25

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• 2

• 1

• -1

• 8

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• A

• B

• C

• D

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• x = -6

• x = 3

• x = 7/3

• x = -5

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• x = -6

• x = 3

• x = 7/3

• No Solution

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• x = -2

• x = 3

• x = 5

• No Solution

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• x = 2

• x = 4

• x = 7

• x = 9

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• -6

• -3

• 6

• 15

Multiple Choice

Solve the radical equation. Don't forget to check your answers!

• 104/5

• 124/5

• 25

• 14/5