holt algebra 2 8-8 solving radical equations and inequalities for a square root, the index of the...
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![Page 1: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/1.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
For a square root, the index of the radical is 2.
Remember!
![Page 2: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/2.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Solve each equation.
Example 1A: Solving Equations Containing One Radical
Subtract 5.
Simplify.
Square both sides.
Solve for x.
Simplify.
Check
![Page 3: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/3.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
7
Example 1B: Solving Equations Containing One Radical
Divide by 7.
Simplify.
Cube both sides.
Solve for x.
Simplify.
Check
Solve each equation.
3
77 5x - 7 84
7=
![Page 4: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/4.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 4A: Solving Equations with Rational Exponents
Solve each equation.
(5x + 7) = 3
Cube both sides.
Solve for x.
Factor.
Write in radical form.
Simplify.5x + 7 = 27
5x = 20
x = 4
13
![Page 5: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/5.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 2: Solving Equations Containing Two Radicals
Square both sides.
Solve
Simplify.
Distribute.
Solve for x.
7x + 2 = 9(3x – 2)
7x + 2 = 27x – 18
20 = 20x
1 = x
![Page 6: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/6.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 3 Continued
Method 2 Use algebra to solve the equation.
Step 1 Solve for x.
Square both sides.
Solve for x.
Factor.
Write in standard form.
Simplify.–3x + 33 = 25 – 10x + x2
0 = x2 – 7x – 8
0 = (x – 8)(x + 1)
x – 8 = 0 or x + 1 = 0
x = 8 or x = –1
![Page 7: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/7.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 3 Continued
Method 2 Use algebra to solve the equation.
Step 2 Use substitution to check for extraneous solutions.
3 –3 6 6 x
Because x = 8 is extraneous, the only solution is x = –1.
![Page 8: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/8.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 2 Use algebra to solve the equation.
Step 1 Solve for x.
Square both sides.
Solve for x.
Factor.
Write in standard form.
Simplify.2x + 14 = x2 + 6x + 9
0 = x2 + 4x – 5
0 = (x + 5)(x – 1)
x + 5 = 0 or x – 1 = 0
x = –5 or x = 1
Check It Out! Example 3a Continued
![Page 9: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/9.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 1 Use algebra to solve the equation.
Step 2 Use substitution to check for extraneous solutions.
4 4 x
Because x = –5 is extraneous, the only solution is x = 1.
Check It Out! Example 3a Continued
2 14 35 5
2 –2
![Page 10: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities For a square root, the index of the radical is 2. Remember!](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d835503460f94a6a23d/html5/thumbnails/10.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
HW pg. 633#’s 27 – 41