Simplifying Radicals: Variables and Exponents

The video tutorial by Mario's Math Tutoring explains how to simplify cube, fourth, and square roots involving variables. It covers breaking down numbers into prime factors and identifying groups of numbers or variables to simplify the expression. The tutorial assumes all variables are positive and provides step-by-step examples for each type of root, emphasizing the importance of finding groups of the same quantity to simplify the radicals.

What is the cube root of 8?

• 2

• 4

• 8

• 16

How many X variables remain under the radical when simplifying the cube root of X to the fifth?

• X to the fifth

• X to the fourth

• X to the third

• X to the second

What does the cube root of Z cubed simplify to?

• Z cubed

• None

• Z squared

• Z

What is the fourth root of 64?

• 8

• 4

• 16

• 2

After simplifying, what exponent does B have in the fourth root of B to the 8th?

• B to the first

• B to the third

• B to the second

• B to the fourth

What remains under the radical when simplifying the fourth root of C to the 11th?

• C to the second

• C to the fourth

• C to the first

• C to the third

What is the result of simplifying the fourth root of A to the first?

• None

• A to the second

• A to the third

• A to the first

What is the square root of 20 simplified?

• 5√2

• 2√10

• 4√5

• 2√5

How many Z variables are left after simplifying the square root of Z to the 12th?

• None

• Z to the first

• Z to the twelfth

• Z to the sixth

What is left under the radical when simplifying the square root of X to the first?

• X to the second

• X to the first

• X to the third

• None