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.

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

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

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

Holt Algebra Solving Radical Equations

Holt Algebra 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 Simplify. Check

Holt Algebra 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

Holt Algebra 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

Holt Algebra 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

Holt Algebra 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.

Holt Algebra 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.

Holt Algebra 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.

Holt Algebra 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.

Holt Algebra 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

Holt Algebra 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.

Holt Algebra 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

Holt Algebra 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

Holt Algebra 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 

Holt Algebra 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.

Holt Algebra 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.

Holt Algebra 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

Holt Algebra Solving Radical Equations Lesson Quiz: Part I Solve each equation. Check your answer no solution

Holt Algebra 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