Simplifying Expressions and Functions

The video tutorial covers simplifying expressions involving square roots and exponents, rationalizing denominators, solving equations with radicals, and graphing radical functions. It also explains how to determine the domain and range of functions with radicals and verifies solutions to radical equations.

What is the simplified form of the expression √18?

• √9

• 3√2

• 2√3

• 6

How do you simplify the expression a^7 / a^3?

• a^10

• a^4

• a^3

• a^5

What is the simplified form of b^6 / b^-4?

• b^0

• b^10

• b^2

• b^4

What is the result of rationalizing the denominator of 8/√2x?

• 8/x

• 4√2/x

• 8√2x/2x

• 4√2x/x

What is the result of rationalizing the denominator of 5/(3-√7)?

• 15 - 5√7 / 2

• 15 + 5√7 / 2

• 5 + √7 / 3

• 5 - √7 / 3

What is the value of x in the equation 3√(2x+6) = 12?

• x = 3

• x = 6

• x = 5

• x = 4

What is the range of the function that shifts one unit left and three units up?

• [3, ∞)

• (-∞, 3]

• [0, 3]

• (-∞, ∞)

What is the simplified form of 3√72 - 4√50 + 7√32?

• 28√2

• 26√2

• 20√2

• 18√2

What is the domain of a function with an even index number in the denominator?

• (0, ∞)

• [0, ∞)

• (-3, 2)

• (-∞, ∞)

How do you solve the equation 3 + √(5-x) = x?

• x = 2

• x = 5

• x = 4

• x = 1