Understanding Radical Equations

This video tutorial covers solving radical equations, focusing on isolating the radical, squaring both sides, solving the resulting equation, and checking for extraneous solutions. It provides step-by-step examples, including handling complex equations and those with radicals on both sides, emphasizing the importance of verifying solutions.

What is the first step in solving a radical equation?

• Square both sides of the equation

• Isolate the radical expression

• Check for extraneous solutions

• Add a constant to both sides

Why is it important to check for extraneous solutions?

• To ensure the solution is valid in the original equation

• To simplify the equation further

• To find additional solutions

• To verify the equation is balanced

In the example where the square root of X equals 9, what is the value of X?

• 81

• 9

• 27

• 18

What should you do if a radical expression is not isolated?

• Square both sides immediately

• Add or subtract terms to isolate the radical

• Ignore the non-isolated terms

• Multiply both sides by a constant

In the equation 5M - 1 = 169, what is the value of M after solving?

• 33

• 35

• 32

• 34

When solving an equation with radicals on both sides, what is the first step?

• Add a constant to both sides

• Isolate one of the radicals

• Square both sides

• Subtract a constant from both sides

What is the solution for the equation where the square root of 2C plus 3 equals 5?

• C = 13

• C = 11

• C = 12

• C = 10

How do you handle an equation with multiple values hanging off a radical expression?

• Multiply all terms by a constant

• Add all values to both sides

• Reverse the operations to isolate the radical

• Ignore the additional values

In the equation r = 42 - 2r, what is the value of r after solving?

• 28

• 14

• 21

• 7

What is the final step in solving a radical equation?

• Add a constant to both sides

• Subtract a constant from both sides

• Check the solution in the original equation

• Multiply both sides by a constant