Solving Radical Equations: Key Concepts and Techniques

The video tutorial introduces solving radical equations, starting with a review of two-step equations using reverse PEMDAS. It progresses through examples involving cube roots, square roots, and rational exponents, emphasizing the importance of order of operations. The tutorial concludes with a complex example involving multiple radicals, highlighting common student errors and strategies for checking solutions.

What is the first step in solving the equation 2x + 4 = -6 using reverse PEMDAS?

• Multiply by 2

• Add 4

• Divide by 2

• Subtract 4

What operation is used to eliminate the cube root in the equation cube root of x - 2 = 0?

• Square rooting

• Cubing

• Addition

• Subtraction

In the equation 3 times the square root of x + 4 - 1 = 8, what is the first operation to perform?

• Square both sides

• Divide by 3

• Add 1

• Subtract 4

What is the value of x when solving the equation 3 times the square root of x + 4 equals 9?

• x = 5

• x = 1

• x = 25

• x = 9

How do you solve for x in the equation x^(3/2) - 2 = 25?

• Divide both sides by 2

• Multiply both sides by 2

• Add 2 to both sides

• Subtract 2 from both sides

What is the result of raising 27 to the power of (2/3)?

• 81

• 9

• 18

• 3

What is the inverse operation used to solve x^(3/2) = 27?

• Cubing

• Square rooting

• Raising to the power of (2/3)

• Raising to the power of (3/2)

What does the square operation do to the square root in the equation square root of 2x - square root of x + 1 = 0?

• Squares it

• Doubles it

• Halves it

• Eliminates it

What is the correct order to solve the equation involving a square root and addition inside the radical?

• Subtraction, then division

• Square root, then addition

• Addition, then square root

• Division, then multiplication

After solving the equation with radicals, what should you do to verify your solution?

• Substitute back into the original equation

• Multiply by the coefficient

• Add the constants

• Divide by the variable