1. Solve Quadratic Equations by Finding Square Roots
Section 4.5:
Solve Quadratic Equations by
Finding Square Roots

2. A number r is a square root of a number s if r2 = s
A number r is a square root of a number s if r2 = s. A positive number s has two square roots, written and The positive square root of a number is also called the principal square root.

3. Radical – the expression
Radical – the expression . The symbol is a radical sign, and the number s beneath the radical sign is the radicand of the expression.

4. Properties of Square Roots (a > 0, b > 0)
Product Property: Example:

5. Rationalizing the Denominator
Form of the denominator
Multiply numerator and denominator by:

6. The expressions and are called conjugates of each other
The expressions and are called conjugates of each other. Their product is always a rational number.

7. Example 1: Simplify the expression. a) b)

8. Properties of Square Roots (a > 0, b > 0)
Quotient Property: Example:

9. c) d)

10. Example 2: Simplify the expression. a) b)

11. HOMEWORK (Day 1)
pg. 269; 3 – 18

12. Example 3: Solve 2x2 – 15 = 65 2x2 = 80 x2 = 40

13. Example 4: Solve

14. Example 5: If you drop an object off the roof of a building that is 240 feet tall, about how long will it take the object to hit the ground? h = -16t2 + h0 h is the height above the ground after t seconds h0 is the initial height t is the time (in seconds)

15. h = -16t2 – h0 0 = -16t2 + 240 -240 = -16t2 15 = t2 t = Time is always positive!

16. HOMEWORK (Day 2)
pg. 270; 20 – 34 even, 38