1. Section 11-5 Solving Radical Equations

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

3. Objectives Standards California
Extension of 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.

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

5. 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.

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

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

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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

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

16. 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

17. 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

18. You try: 1) 2)
x = 2

19. 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

20. : 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.

21. 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 feet.
82 = x

22. 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.

23. 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.