Section 11-5 Solving Radical Equations

Warm Up Solve each equation. 1. 3x +5 = 17 2. 4x + 1 = 2x – 3 4 3. –2 35 –7, 4 6, 5 5, –3

Objectives Standards California Extension of 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

Vocabulary radical equation A radical equation is an equation that contains a variable within a radical.

Solving Simple Radical Equations Solve the equation. Check your answer. Square both sides. x = 25 Check Substitute 25 for x in the original equation. 5 5  Simplify.

Solving Simple Radical Equations Solve the equation. Check your answer. Square both sides. 100 = 2x Divide both sides by 2. 50 = x Check 10 10 

Lets Try Together:  Solve the equation. Check your answer. Square both sides. Simplify. Check  6 6

You try: Solve the equation. Check your answer. 1) 2) 3) 3 = x x = 12

Solving Simple Radical Equations To solve these equations, you may have to isolate the square root +4 +4 Add 4 to both sides. Square both sides. x = 81

Solving Simple Radical Equations To solve these equations, you may have to isolate the square root Square both sides. Subtract 3 from both sides. -3 -3 x = 46

5x + 1 = 16 5x = 15 Lets try together: -6 -6 -1 -1 x = 3 To solve these equations, you may have to isolate the square root Subtract 6 from both sides. -6 -6 Square both sides. Subtract 1 from both sides. 5x + 1 = 16 -1 -1 5x = 15 Divide both sides by 5. x = 3

x = 9 x = 18 x = 3 1) 2) 3) You Try: Solving Simple Radical Equations To solve these equations, you may have to isolate the square root 1) 2) 3) x = 9 x = 18 x = 3

Solving Radical Equations by Multiplying or Dividing Method 1 Method 2 Square both sides. Divide both sides by 4. Square both sides. Divide both sides by 16. x = 64 x = 64

Solving Radical Equations by Multiplying or Dividing Method 1 Method 2 Multiply both sides by 2. Square both sides. Square both sides. 144 = x Multiply both sides by 4. 144 = x

You try 1) 2) 3) 64 = x x = 100

Solving Radical Equations with Square Roots on Both Sides Square both sides. 2x – 1 = x + 7 -x -x +1 +1 Add 1 to both sides and subtract x from both sides. x = 8

Solving Radical Equations with Square Roots on Both Sides Add to both sides. Square both sides. 5x – 4 = 6 Add 4 to both sides. +4 +4 5x = 10 x = 2

You try: 1) 2) x = 2

Lesson Quiz ø Solve each equation. Check your answer. 1. 36 2. 45 3. 4. 11 5. 4 6. 4 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

: Geometry Application: Example 1 A triangle has an area of 36 square feet, its base is 8 feet, and its height is feet. What is the value of x? What is the height of the triangle? 8 ft Use the formula for area of a triangle. Substitute 8 for b, 36 for A, and for h. Simplify. Divide both sides by 4.

The height of the triangle is 9 feet. Example 1: Continued A triangle has an area of 36 square feet, its base is 8 feet, and its height is feet. What is the value of x? What is the height of the triangle? 8 ft Square both sides. 81 = x – 1 The value of x is 82. The height of the triangle is 9 feet. 82 = x

Geometry Application: Example 2 A rectangle has an area of 15 cm2. 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. Substitute 5 for w, 15 for A, and for l. Divide both sides by 5.

9= x+1 Example 2: continued A rectangle has an area of 15 cm2. 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. 9= x+1 The value of x is 8. The length of the rectangle is cm.