Simplifying Cube Root Expressions

The video tutorial explains how to simplify the cube root of a complex expression. It begins by identifying perfect cubes within the expression, such as the number 8, and then focuses on simplifying variables by breaking them into perfect cubes and non-perfect cubes. The tutorial demonstrates how to rewrite the expression by taking cube roots of perfect cubes and leaving the rest under the radical. The final simplified form is presented, highlighting the process of factoring and simplifying cubic radicals.

What is the first step in simplifying a cube root expression?

• Divide the expression by 2.

• Add all the terms inside the radical.

• Factor the expression into perfect cubes and non-perfect cubes.

• Multiply all the terms inside the radical.

How can the number 8 be expressed as a perfect cube?

• 8 is 2 times 2 times 2.

• 8 is 5 times 1.6.

• 8 is 3 times 3.

• 8 is 4 times 2.

What is the cube root of 8?

• 1

• 2

• 3

• 4

How can b to the fifth be rewritten to identify a perfect cube?

• b to the fifth is b squared times b cubed.

• b to the fifth is b cubed times b squared.

• b to the fifth is b to the fourth times b.

• b to the fifth is b times b to the fourth.

Which of the following is already a perfect cube?

• b to the fifth

• c to the third

• b squared

• a squared

What is the cube root of b cubed?

• b

• b squared

• b to the fourth

• b to the fifth

What is the cube root of c to the third?

• c to the fourth

• c to the fifth

• c

• c squared

Which part of the expression remains under the cube root after simplification?

• a squared b squared

• a cubed b cubed

• a b

• a to the fourth b to the fourth

What is the final simplified form of the cube root expression?

• 2abc times the cube root of a squared b squared

• 2c times the cube root of a squared b squared

• abc times the cube root of a squared b squared

• 2ab times the cube root of a squared b squared

What is the main goal when simplifying a cube root expression?

• To add more terms to the expression.

• To express the cube root in its simplest form.

• To factor the expression into smaller terms.

• To make the expression longer.