11 9 Solving Radical Equations Warm UpAdd to

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11 -9 Solving Radical Equations Warm Up(Add to Hw) Solve each equation. 1. 3

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

11 -9 Solving Radical Equations Holt Algebra 11

11 -9 Solving Radical Equations Holt Algebra 11

11 -9 Solving Radical Equations A radical equation is an equation that contains a

11 -9 Solving Radical Equations A radical equation is an equation that contains a variable within a radical. Holt Algebra 1

11 -9 Solving Radical Equations Holt Algebra 1

11 -9 Solving Radical Equations Holt Algebra 1

11 -9 Solving Radical Equations Example 1 A: Solving Simple Radical Equations Solve the

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

11 -9 Solving Radical Equations Check It Out! Example 1 b Solve the equation.

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

11 -9 Solving Radical Equations Example 2 A: Solving Simple Radical Equations Solve the

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

11 -9 Solving Radical Equations Example 2 B: Solving Simple Radical Equations Solve the

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

11 -9 Solving Radical Equations Example 2 C: Solving Simple Radical Equations Solve the

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

11 -9 Solving Radical Equations Example 3 A: Solving Radical Equations by Multiplying or

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

11 -9 Solving Radical Equations Example 3 B: Solving Radical Equations by Multiplying or

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

11 -9 Solving Radical Equations Check It Out! Example 3 c Solve the equation.

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

11 -9 Solving Radical Equations Example 4 A: Solving Radical Equations with Square Roots

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

11 -9 Solving Radical Equations Example 4 B: Solving Radical Equations with Square Roots

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

11 -9 Solving Radical Equations Squaring both sides of an equation may result in

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. Holt Algebra 1 x=3 x 2 = 9 x = 3 or x = – 3

11 -9 Solving Radical Equations Example 5 A: Extraneous Solutions Solve Check your answer.

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

11 -9 Solving Radical Equations Example 5 A Continued Solve Check your answer. Check

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

11 -9 Solving Radical Equations Check It Out! Example 6 A rectangle has an

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? A = lw Use the formula for area of a rectangle. Substitute 5 for l, 15 for A and for w. Divide both sides by 5. Holt Algebra 1 5

11 -9 Solving Radical Equations Check It Out! Example 6 Continued A rectangle has

11 -9 Solving Radical Equations 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 Square both sides. 8=x The value of x is 8. The length of the rectangle is cm. Holt Algebra 1

11 -9 Solving Radical Equations Check It Out! Example 6 Continued A rectangle has

11 -9 Solving Radical Equations 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? Check A = lw Substitute 8 for x. 15 Holt Algebra 1 15 5

11 -9 Solving Radical Equations Lesson Quiz: Part I Solve each equation. Check your

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

11 -9 Solving Radical Equations Lesson Quiz: Part II 7. A triangle has an

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 Holt Algebra 1

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