Solving Radical Equations and Square Roots

The video tutorial explains how to solve radical equations with one radical by isolating the radical, raising both sides to the power of the index, solving the resulting equation, and checking the solutions. Two examples are provided: one with the square root of 2x - 7 = 9 and another with the square root of x + 3 = -3 + 8. Each example demonstrates the process of isolating the radical, squaring both sides, solving the linear equation, and verifying the solution by substitution.

What is the first step in solving a radical equation with one radical?

• Subtract a constant from both sides

• Multiply both sides by the index

• Isolate the radical on one side

• Add a constant to both sides

What operation is used to eliminate a square root in an equation?

• Multiplying by the index

• Squaring both sides

• Taking the cube root

• Dividing by the index

In the first example, what is the value of x after solving the equation?

• 22

• 44

• 81

• 9

How do you verify the solution of a radical equation?

• By using a calculator

• By graphing the equation

• By solving a different equation

• By checking if the solution satisfies the original equation

What is the square root of 81?

• 8

• 7

• 9

• 10

What is the first step in the second example to isolate the square root?

• Subtract 8 from both sides

• Add 8 to both sides

• Divide both sides by 2

• Multiply both sides by 2

What is the result of squaring 5 in the second example?

• 10

• 5

• 25

• 15

In the second example, what is the final value of x?

• 25

• 22

• 5

• 3

What is the purpose of substituting the solution back into the original equation?

• To find a new solution

• To verify the solution

• To simplify the equation

• To eliminate the radical

What is the square root of 25?

• 6

• 5

• 4

• 3