Exploring Operations with Radicals

This video tutorial covers section 6.5 on operations with radicals. It begins with an overview of the objectives, which include adding, subtracting, multiplying, and dividing radicals. The tutorial provides detailed explanations and examples for simplifying radicals, using the product property for multiplication, and combining like radicals. It also covers multiplying binomials with radicals using the FOIL method and rationalizing denominators when dividing radicals. The video concludes with a discussion on using conjugates to rationalize denominators, ensuring a comprehensive understanding of operations with radicals.

What is the first step in simplifying the radical expression √12c^6d^3?

• Find the largest perfect square factor of 12

• Divide the exponents of the variables by 3

• Multiply the coefficients

• Add the exponents of the variables

When multiplying radicals, what property allows you to combine the square roots of two numbers?

• Difference Property

• Sum Property

• Product Property

• Quotient Property

What is the simplified form of 6√8c^3d^5?

• 96c^2d^4

• 24c^2d^4

• 96√2c^2d^4

• 24√2c^2d^4

Which of the following pairs of radicals can be added together?

• √7 and √7

• 2√2 and 3√2

• 4√3 and 4√5

• √3 and √5

Simplify the expression 4√8 + 3√50.

• 23√2

• 12√58

• 8√2 + 15√2

• 7√58

What is the first step in multiplying binomials that contain radicals?

• Combine like terms

• Rationalize the denominator

• Simplify the radicals

• Use the FOIL method

What is the result of multiplying (6√3 - 5) and (2√5 + 4√2)?

• 12√15 + 24√6 - 10√5 + 20√2

• 12√15 + 24√6 - 10√5 - 20√2

• 12√15 - 24√6 + 10√5 + 20√2

• 12√15 - 24√6 + 10√5 - 20√2

What property allows you to separate the square root of a fraction into the square root of the numerator and the square root of the denominator?

• Difference Property

• Sum Property

• Quotient Property

• Product Property

How do you rationalize the denominator of a fraction with a binomial containing a radical?

• Divide the numerator by the denominator

• Multiply by the conjugate of the denominator

• Add the numerator and denominator

• Subtract the numerator from the denominator

Simplify the expression (2/√5 - 1) by rationalizing the denominator.

• √5 + 2

• √5 - 2

• 2√5 - 1

• 2√5 + 1