Simplifying Radicals in Denominators

What is a conjugate in the context of binomial expressions with radicals?

• A completely different expression

• A term with the same radical but a different coefficient

• A term with the opposite sign and the same radical component

• A term with the same sign and a different radical component

What is achieved by switching the sign in a conjugate?

• Eliminating the radical from the denominator

• Changing the value of the radical

• None of the above

• Creating a complex number

Why do we multiply by the conjugate in the process of simplifying radicals?

• To eliminate the radical from the denominator

• To increase the complexity of the expression

• To change the sign of the radical

• To balance the equation

What mathematical operation is primarily used in the process described in the video?

• Addition

• Multiplication

• Subtraction

• Division

What happens to the square roots when we multiply by the conjugate?

• They remain unchanged

• They are multiplied by two

• They cancel each other out

• They are squared

What is the result of multiplying -3 by the square root of 8?

• -24

• 24

• 3 root 8

• -3 root 8

What is the simplified form of the square root of 8?

• 2 root 4

• 4 root 2

• 2 root 2

• 8 root 1

What does the numerator become after combining like terms in the final steps?

• 0

• 56

• 24

• 16

What is the final simplified form of the expression?

• 5 root 4

• 5 root 2

• 10 root 2

• 10 root 4

How is the square root of 8 further simplified in the final steps?

• 2 root 2

• 4 root 2

• Root 16

• 8