1. Solving Square Root and Other Radical Equations
What you’ll learn
Solve square root and other radical equations .
Vocabulary
Radical Equation: Any equation that includes a
variable inside a radicand (or with a fractional exponent)
Square root equation: To solve radical equations, isolate the radical on one side of the equal sign, and raise both sides of the equation to the necessary power to remove the radical sign

2. Problem 1: Solving a Square root Equation What is the solution of
Isolate the radical
Square each side,
Remember you don’t need ±,
Because you are squaring both sides
Then isolate the x by adding 3 and dividing by 2
Check your answer:

3. Your turn Solve: Answer: 7,6
Take a note: You can solve equations of the form by raising each side of the equation to the power the reciprocal of If either m or n is even, then
If the nth root of an expression that contains an nth power as a factor cam be simplified

4. Problem 2:Solving Other Radicals Equations
Answer
Divide each side by 3
Raise each side to
Check your solution

5. Your turn
Answer:31
Answers: 5,-11

6. For meteor Crater in Arizona, the formula
Your turn again
For meteor Crater in Arizona, the formula
Relates the diameter d of the rim in meters to the
volume V in cubic meters. What is the volume of
meteor crater? All values are approximate.
Answer
1.2 km

7. Problem 3: Checking for extraneous solutions
When you raise each side of an equation to a power, it is possible to introduce extraneous solutions in the original equation, it becomes
very important to check all solutions in the original equation. A
Correct solution will give you a true statement. An extraneous
solution will give you a false statement.
Problem 3: Checking for extraneous solutions
Answer
Isolate the radical
Square each side
Simplify
Combine like terms
Factor

8. Remember check your answers
You can use the graphing calculator to verify your answers
Graph From the graph it is
clear that -3 is a solution and -6 is not..
Your turn
Answer: 10

9. Problem 4: Solving an Equation with two Radicals
Isolate the more complicated radical
Square each side
Solve, combine like terms
Square each side
Check

10. Your turn
Answer: 9

11. Classwork odd Homework even
TB pgs exercises 9-67