1. Holt Algebra 1 11-9 Solving Radical Equations Warm Up(Add to Hw) Solve each equation. 1. 3x +5 = 17 2. 4x + 1 = 2x – 3 3. 4. (x + 7)(x – 4) = 0 5. x 2 – 11x + 30 = 0 4 –2 35 –7, 4 6, 5

2. Holt Algebra 1 11-9 Solving Radical Equations 11-9Solving Radical Equations Holt Algebra 1

3. 11-9 Solving Radical Equations A radical equation is an equation that contains a variable within a radical.

4. Holt Algebra 1 11-9 Solving Radical Equations

5. Holt Algebra 1 11-9 Solving Radical Equations Example 1A: Solving Simple Radical Equations Solve the equation. Check your answer. x = 25 Square both sides. Substitute 25 for x in the original equation. 55 5 Simplify. Check

6. Holt Algebra 1 11-9 Solving Radical Equations Check It Out! Example 1b Solve the equation. Check your answer. 81 = 27x 3 = x Square both sides. Divide both sides by 27. Substitute 3 for x in the original equation. Simplify. Check

7. Holt Algebra 1 11-9 Solving Radical Equations Example 2A: Solving Simple Radical Equations Solve the equation. Check your answer. x = 81 Add 4 to both sides. Square both sides. Check 9 – 4 5 5

8. Holt Algebra 1 11-9 Solving Radical Equations Example 2B: Solving Simple Radical Equations Solve the equation. Check your answer. x = 46 Subtract 3 from both sides. Square both sides. Check 7

9. Holt Algebra 1 11-9 Solving Radical Equations Example 2C: Solving Simple Radical Equations Solve the equation. Check your answer. 5x + 1 = 16 5x = 15 x = 3 Subtract 6 from both sides. Square both sides. Subtract 1 from both sides. Divide both sides by 5.

10. Holt Algebra 1 11-9 Solving Radical Equations Example 3A: Solving Radical Equations by Multiplying or Dividing Solve the equation. Check your answer. x = 64 Divide both sides by 4. Square both sides.

11. Holt Algebra 1 11-9 Solving Radical Equations Example 3B: Solving Radical Equations by Multiplying or Dividing Solve the equation. Check your answer. 144 = x Square both sides. Multiply both sides by 2.

12. Holt Algebra 1 11-9 Solving Radical Equations Check It Out! Example 3c Solve the equation. Check your answer. Square both sides. Multiply both sides by 5. x = 100 Divide both sides by 4.

13. Holt Algebra 1 11-9 Solving Radical Equations Example 4A: Solving Radical Equations with Square Roots on Both Sides Solve the equation. Check your answer. 2x – 1 = x + 7 x = 8 Square both sides. Add 1 to both sides and subtract x from both sides. Check

14. Holt Algebra 1 11-9 Solving Radical Equations Example 4B: Solving Radical Equations with Square Roots on Both Sides Solve the equation. Check your answer. 5x – 4 = 6 5x = 10 x = 2 Add to both sides. Square both sides. Add 4 to both sides. Divide both sides by 2.

15. Holt Algebra 1 11-9 Solving Radical Equations Squaring both sides of an equation may result in an extraneous solution—a number that is not a solution of the original equation. Suppose your original equation is x = 3. Square both sides. Now you have a new equation. Solve this new equation for x by taking the square root of both sides. x = 3 x 2 = 9 x = 3 or x = –3

16. Holt Algebra 1 11-9 Solving Radical Equations Example 5A: Extraneous Solutions Solve Check your answer. Square both sides Divide both sides by 6. Subtract 12 from each sides. 6x = 36 x = 6

17. Holt Algebra 1 11-9 Solving Radical Equations Example 5A Continued Solve Check your answer. Substitute 6 for x in the equation. Check 6 does not check. There is no solution. 18 6 

18. Holt Algebra 1 11-9 Solving Radical Equations Check It Out! Example 6 A rectangle has an area of 15 cm 2. Its width is 5 cm, and its length is ( ) cm. What is the value of x? What is the length of the rectangle? 5 A = lw Use the formula for area of a rectangle. Divide both sides by 5. Substitute 5 for l, 15 for A and for w.

19. Holt Algebra 1 11-9 Solving Radical Equations Check It Out! Example 6 Continued 8 = x Square both sides. A rectangle has an area of 15 cm 2. Its width is 5 cm, and its length is ( ) cm. What is the value of x? What is the length of the rectangle? 5 The value of x is 8. The length of the rectangle is cm.

20. Holt Algebra 1 11-9 Solving Radical Equations CheckA = lw 15 Substitute 8 for x. Check It Out! Example 6 Continued A rectangle has an area of 15 cm 2. Its width is 5 cm, and its length is ( ) cm. What is the value of x? What is the length of the rectangle? 5

21. Holt Algebra 1 11-9 Solving Radical Equations Lesson Quiz: Part I Solve each equation. Check your answer. 1. 3. 5. 2. 4. 6. 36 45 no solution 11 4 4

22. Holt Algebra 1 11-9 Solving Radical Equations Lesson Quiz: Part II 7. A triangle has an area of 48 square feet, its base is 6 feet and its height is feet. What is the value of x? What is the height of the triangle? 253; 16 ft