Simplifying Radicals with Variables

This video tutorial covers simplifying radicals with variables, starting with a review of exponent properties. It explains the concept of fractional powers and their equivalence to square roots. The tutorial then applies these concepts to variables, demonstrating how to simplify radicals with even and odd powers. Through a series of examples, the video provides a detailed walkthrough of the simplification process, emphasizing the identification of perfect squares and the application of these techniques to both numerical and variable expressions.

What happens to the base when you decrease the power by one in an exponent?

• You add one factor of the base.

• You lose one factor of the base.

• You multiply the base by itself.

• The base remains the same.

What is the square root of a number equivalent to in terms of exponents?

• The number raised to the power of 2.

• The number multiplied by 1/2.

• The number raised to the power of 1/2.

• The number divided by 2.

What is the square root of 36?

• 12

• 6

• 18

• 8

What is the square root of x^4?

• x^2

• x^3

• x^5

• x

What is the square root of x^20?

• x^8

• x^5

• x^10

• x^15

How do you simplify the square root of an odd-powered variable like B^7?

• Rewrite it as a product with the smallest perfect square factor.

• Multiply the power by 2.

• Rewrite it as a product with the largest perfect square factor.

• Divide the power by 2.

What is the simplified form of the square root of x^5?

• x^2 * sqrt(x)

• x^3 * sqrt(x)

• x * sqrt(x)

• x^4 * sqrt(x)

What is the simplified form of the square root of 16y^2?

• 2y

• 8y

• 16y

• 4y

How do you simplify the square root of 25y^3?

• 5y^2

• 5y * sqrt(y)

• 5y^2 * sqrt(y)

• 5 * sqrt(y)

What is the simplified form of the square root of 64x^3y^5z^3?

• 8x^2y^2z^2 * sqrt(xyz)

• 8x^2y^2z * sqrt(xyz)

• 8xy^2z^2 * sqrt(xyz)

• 8xy^2z * sqrt(xyz)