Radical Expressions and Simplification

The video tutorial explains how to multiply radical expressions by distributing terms and simplifying the results. It covers three examples: the first involves multiplying a single radical expression with a sum of terms, the second focuses on multiplying radicals with perfect square factors, and the third deals with cube roots and their simplification. The tutorial emphasizes the importance of identifying perfect squares and cubes to simplify expressions and discusses when to use absolute values.

What is the first step in multiplying a radical expression with a sum or difference of terms?

• Subtract the terms from each other.

• Add the terms together.

• Distribute the radical expression across the terms.

• Combine the terms under a single radical.

When multiplying radicals, what should you do with the radicands?

• Subtract them.

• Divide them.

• Add them together.

• Multiply them.

Why is it necessary to include an absolute value when simplifying certain square roots?

• Because the index is odd.

• Because the radicand is negative.

• Because the index is even and the exponent is odd.

• Because the radicand is a fraction.

What is the result of multiplying 4√y by 5√xy?

• 20√xy^2

• 20√x^2y

• 20√xy^4

• 20√y^2

How do you simplify the square root of y^4?

• By writing it as y.

• By writing it as y^2.

• By writing it as y^3.

• By writing it as y^2 * y^2.

What is the first step in multiplying cube roots?

• Subtract the radicands.

• Add the radicands.

• Divide the radicands.

• Multiply the radicands.

Which of the following is a perfect cube?

• z^5

• z^4

• z^3

• z^2

What is the cube root of z^9 simplified to?

• z^3

• z^2

• z

• z^4

Why is no absolute value needed when simplifying cube roots?

• Because the index is even.

• Because the radicand is always positive.

• Because the index is odd.

• Because the radicand is a fraction.

What is the final product when simplifying the cube root of z^3?

• z^4

• z^2

• z

• z^3