1. 5.3 Solving Quadratic Equations
by Finding Square Roots

2. What is a Square Root?
 The opposite of squaring a number.
 r is the square root of s if r2 = s
 Positive numbers have two square
roots: and –
 is called a radical sign
 The number inside is the radicand
 The expression is a radical

3. Properties of Square Roots
 Product Property:
 Example:
 Used to simplify radical expressions.

4. Simplifying Radical Expressions
 Using the Product Property:
1. Try to find a “perfect square” that is a
factor.
2. Rewrite as a product of two radicals.
3. Take the square root of the perfect
square.
Example: Simplify

5. Examples
 Simplify each radical expression:

6. Your Turn!
 Simplify each radical expression.

7. Properties of Square Roots
 Quotient Property:
 Example:

8. Simplifying Radical Expressions
 Using the Quotient Property:
1. Rewrite as a quotient of two radicals.
We can’t leave a square root on the bottom!
 If bottom is a perfect square:
1. Take square roots on top and bottom.
2. Simplify the top if needed.
 If bottom is not a perfect square:
1. Multiply by the denominator over itself.
2. Simplify.
◦ Called “Rationalizing the Denominator”

9. Examples:
Simplify each radical expression.

10. Your Turn!
 Simplify each radical expression.

11. Solving Equations
 Square roots can be used to solve some
quadratic equations.
 For example: has two
solutions,
 Usually written
  is read “plus or minus”

12. To Solve:
 Get the squared part by itself.
 Take the square root of both sides.
 Simplify your answer - NO DECIMALS!
 Don’t forget the  !

13. Examples:
 Solve
 Solve

14. Your Turn!
 Solve:

15. Solving Quadratics with ( )
 Get the squared part by itself.
 Take the square root of both sides.
 Then, keep solving to get x alone.
 Example: Solve (x – 2)2 = 36

16. Examples:
Solve:
3(x + 5)2 = 24
(2x – 1)2 = 49 (x - 7)2 = 80

17. Your Turn!
 Solve:
(x + 6)2 = 81

18. Using Quadratic Models
 On Earth, when an object is dropped, its
height h (in feet), t seconds after being
dropped, can be modeled by:
where is the object’s initial height
(note: this model neglects air resistance)

19. Example:
 How long will it take an object dropped
from a 550-foot tall tower to land on
the roof of a 233-foot tall building?