This document discusses solving radical expressions and quadratic equations by taking square roots. It covers the properties of square roots including the product and quotient properties. Examples are provided of simplifying radical expressions using these properties as well as solving quadratic equations by taking square roots. The document also provides an example of modeling the height of a falling object using a quadratic equation.

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. Example:
 Solve
 Solve

13. Your Turn!
 Solve:

14. 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)

15. 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?