Simplifying Radical Expressions

The video tutorial covers simplifying radical expressions involving variables. It begins with an introduction to the concept, followed by detailed steps on multiplying and simplifying radicals by extracting perfect squares. The tutorial includes examples with single and multiple variables, demonstrating the application of exponent properties and the importance of factoring in simplifying radicals.

What is the first step in simplifying a radical expression involving variables?

• Divide the coefficients by the radicals.

• Multiply the coefficients and simplify the radicals separately.

• Add all the coefficients together.

• Subtract the radicals from the coefficients.

When simplifying the expression 2 * √(7x) * 3 * √(14x^2), what is the result of multiplying the coefficients?

• 5

• 6

• 8

• 7

In the expression √(49x^2), what is the simplified form?

• x^2

• 7x^2

• 7x

• 49x

What is the principal root of 4 in the expression √(4a^4)?

• 3

• 2

• 4

• 1

In the expression √(35a), which part is not a perfect square?

• 7

• 5

• a

• 35

What is the result of multiplying √(2a) and √(14a^3)?

• √(28a^2)

• √(28a^4)

• √(28a^3)

• √(28a^5)

How can the expression √(72x^3z^3) be simplified by factoring out perfect squares?

• 12xz

• 6xz√(2xz)

• 72x^3z^3

• 36x^2z^2

What is the simplified form of √(36x^2)?

• 36x

• 6x^2

• 6x

• x^2

Which of the following is a perfect square in the expression √(72x^3z^3)?

• z^3

• 36

• x^3

• 72

What is the simplified form of √(x^2z^2)?

• xz^2

• x^2z

• x^2z^2

• xz