Simplifying Radical Expressions with Variables

This video tutorial demonstrates how to simplify radical expressions involving variables. It covers two examples: the first involves simplifying the square root of a complex expression, and the second focuses on another expression with different variables. The instructor explains the process of rewriting radicals as rational exponents, distributing exponents, and simplifying the expressions step-by-step. The video emphasizes understanding the conversion between radical and exponential forms and provides tips for handling fractional exponents.

What is the first step in simplifying the expression \(\sqrt{24x^3y^4z^5}\)?

• Combine like terms

• Factor the numerical part

• Distribute the exponents

• Convert the square root to a rational exponent

How can a square root be expressed as a rational exponent?

• As an exponent of 1/3

• As an exponent of 2

• As an exponent of 3

• As an exponent of 1/2

When distributing the exponent \(\frac{1}{2}\) to \(24x^3y^4z^5\), what is the exponent of \(x\)?

• 1/3

• 3/2

• 1/2

• 3

What is the simplified form of \(24^{1/2}\)?

• 12

• 6

• 4

• 2\sqrt{6}

How do you rewrite \(x^{3/2}\) as a mixed number?

• 1 + 1/2

• 2 + 1/2

• 3 + 1/2

• 1 + 1/3

What is the simplified form of \(\sqrt{24x^3y^4z^5}\) in radical notation?

• 2\sqrt{6}xy^2z^2\sqrt{z}

• 2\sqrt{6}x^2y^2z^2

• 2\sqrt{6}x^2y^2z^2\sqrt{z}

• 2\sqrt{6}x\sqrt{x}y^2z^2\sqrt{z}

In the second example, what is the first step in simplifying \(\sqrt{9u^7v^2z}\)?

• Convert the square root to a rational exponent

• Combine like terms

• Distribute the exponents

• Factor the numerical part

What is the simplified form of \(9^{1/2}\)?

• 6

• 3

• 1

• 2

How do you rewrite \(u^{7/2}\) as a mixed number?

• 2 + 1/2

• 1 + 1/2

• 3 + 1/3

• 3 + 1/2

What is the final simplified form of \(\sqrt{9u^7v^2z}\) in radical notation?

• 3u^3v^2\sqrt{z}

• 3u^3v\sqrt{uz}

• 3u^3v\sqrt{u}z

• 3u^3v\sqrt{z}