Simplifying Radicals with Variables

This video tutorial extends the concept of simplifying radicals to include variables. It begins by reviewing perfect squares and exponents, emphasizing the rule that variables with even exponents are perfect squares. The tutorial provides examples of simplifying radicals with variables, demonstrating how to handle both even and odd exponents. The 'subtract one' rule is introduced for odd exponents, allowing students to simplify expressions by breaking them into manageable parts. The video concludes with practice problems and encourages students to use IXL for further practice.

What is the square root of x to the fourth power?

• x cubed

• x squared

• x to the fourth

• x

Which of the following is a perfect square?

• x to the fifth

• x to the sixth

• x to the seventh

• x to the eighth

What is the general rule for variables with even exponents?

• They are perfect squares only if the base is even.

• They are never perfect squares.

• They are always perfect squares.

• They are sometimes perfect squares.

What is the square root of 9?

• 4.5

• 3

• 1.5

• 2

How do you handle odd exponents when simplifying radicals?

• Add one to the exponent.

• Multiply the exponent by two.

• Subtract one from the exponent.

• Divide the exponent by two.

What is the square root of x to the seventh power?

• x to the fifth times radical x

• x to the fourth times radical x

• x squared times radical x

• x cubed times radical x

What is the square root of 50?

• 25 radical 2

• 2 radical 25

• 5 radical 2

• 10 radical 5

How do you simplify the square root of x to the ninth power?

• x to the fifth times radical x

• x squared times radical x

• x to the fourth times radical x

• x cubed times radical x

What is the square root of 200?

• 2 radical 100

• 10 radical 2

• 20 radical 5

• 5 radical 20

What is the final simplified form of the square root of 99 times x to the third times y to the seventh?

• 3x y squared radical 11xy

• 3x squared y cubed radical 11xy

• 3xy cubed radical 11xy

• 3x squared y squared radical 11xy