Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and...
-
Upload
della-welch -
Category
Documents
-
view
220 -
download
0
Transcript of Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and...
![Page 1: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/1.jpg)
Ch 10.3Solving Radical Equations
Objective:
To solve equations involving square roots (and equations involving perfect
squares).
![Page 2: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/2.jpg)
Definitions
Radical Equation:
An equation involving the radical/square root symbol √
Extraneous Solution:
A solution that is NOT valid
![Page 3: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/3.jpg)
Steps for Solvingradical (√) equations
1. Isolate the radical using the reverse order of operations.
2. Square both sides (the radical & the squared symbol cancel each other out)
3. Isolate the variable on one side & solve
4. Check your answers for extraneous solutions.
![Page 4: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/4.jpg)
Equations with Extraneous SolutionsNote: The solution obtained by squaring both sides of the equation is not valid in the original equation.
Check:
No solution
Problem!
An isolated radical cannot equal a negative!
![Page 5: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/5.jpg)
Examples of Radical Equations
1) 2)
3) 4)
![Page 6: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/6.jpg)
5) 6)
More examples of Radical Equations
![Page 7: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/7.jpg)
Solve. Check for extraneous solutions.
7)
![Page 8: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/8.jpg)
Solve. Check for extraneous solutions.
8)
![Page 9: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/9.jpg)
Steps for SolvingSquared ( )² equations
1. Isolate the variable on one side.
2. If it is squared, take the square root (√) of both sides.
3. Add the +/- sign in front of one of the square root symbols (±√)
For example: 2 + x² = 6Step 1 -2 -2
x² = 4Step 2 √x² = ±√4 x =
±2
![Page 10: Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649da05503460f94a8b100/html5/thumbnails/10.jpg)
Solve the Rational Equations. Check for extraneous solutions.
Solve.
One Solution
Two Solutions