Rational Exponents and Radical Equations

The video tutorial covers solving radical equations, starting with an introduction to radicals and their domains. It explains the steps to solve radical equations, including isolating the radical and checking for extraneous solutions. The tutorial also addresses solving quadratic and higher degree radical equations, as well as equations with rational exponents. Complex problems are tackled, emphasizing the importance of verifying solutions.

What is the domain of a square root function?

• Negative infinity to positive infinity

• Zero to positive infinity

• Negative infinity to zero

• Zero to one

Which type of radical equation is more likely to have extraneous solutions?

• Square root equations

• Neither have extraneous solutions

• Cube root equations

• Both have equal likelihood

What is the first step in solving a radical equation?

• Check for extraneous solutions

• Isolate the radical

• Raise both sides to the nth power

• Solve for the variable

When solving the equation √(x-2) = 7, what is the value of x?

• 45

• 53

• 51

• 49

In the equation √(2x-1) = -3, why is there no solution?

• The square root of a negative number is undefined

• The square root cannot be negative

• The variable x is not present

• The equation is not properly isolated

What does a rational exponent represent?

• A fraction in the exponent

• A negative exponent

• An imaginary number

• A whole number exponent

How do you solve x^(1/2) = 10?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 2 from both sides

• Raise both sides to the power of 2

What is the solution to the equation 2x^(3/2) = 250?

• 125

• 100

• 50

• 25

In solving x - 1 = 16^(5/2), what is the value of x?

• 127

• 125

• 126

• 124

Why might a solution be considered extraneous?

• It is greater than 100

• It does not satisfy the original equation

• It is a complex number

• It is a negative number