Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the basics of working with radicals, including adding, subtracting, and multiplying them. It explains how to simplify radicals, combine like terms, and handle radicals with variables. The tutorial also demonstrates the product rule for multiplying radicals and provides examples of multiplying binomials, as well as calculating area and perimeter.

What is the first step in simplifying radicals?

• Identify the radicand

• Multiply the coefficients

• Simplify all radicals

• Combine like terms

When can radicals be combined?

• When they are both cube roots

• When they have the same index and radicand

• When they have the same coefficient

• When they are both square roots

What is the simplified form of 9√3 - 4√3?

• 5√3

• 12√3

• 13√3

• √3

How do you simplify the square root of 98x^4y^2?

• 14x^2y

• 7xy√2

• 49x^2y

• 7x^2y√2

What is the cube root of -40a^7 simplified?

• -2a^3∛5a

• -2a^2∛5a

• -2a^2∛5

• -2a^2√5a

What is the product rule for multiplying radicals?

• Multiply the coefficients and add the radicands

• Multiply the coefficients and multiply the radicands

• Add the coefficients and multiply the radicands

• Add the coefficients and add the radicands

What is the simplified form of 3√10 * -2√18?

• -6√28

• -6√180

• -36√5

• -36√180

What is the result of multiplying (7√6 + 3)(4 - √6)?

• 28√6 - 7√36 + 12 - √18

• 28√6 - 7√36 + 4√3 - 3√2

• 28√6 - 7√36 + 4√3 - √18

• 28√6 - 7√36 + 12√3 - √18

How do you find the perimeter of a rectangle with dimensions involving radicals?

• Square the lengths and widths

• Use the formula 2(length + width)

• Multiply the lengths and widths

• Add the lengths and widths directly

What is the simplified form of (4 - √5)^2?

• 16 - 4√5 + 25

• 16 - 8√5 + 5

• 16 - 4√5 + 5

• 16 - 8√5 + 25