Section 5-6: Solving quadratic equations by finding square roots

1. Section 5-6: Solving quadratic equations by finding square roots Goal: Solving quadratic equations by finding square roots

2. Square root • A number b is a square root of a number a if b2 = a. • A positive number a has two square roots written √a and -√a. For example 22 = 4 and (-2)2 = 4 the two square roots of 4 are √4 = 2 and - √4 = -2. • √a is a radical • √ is a radical sign • The number a beneath the radical symbol is the radicand

4. Simplifying square roots • No radicand has a perfect square factor other than 1 • There is no radical in a denominator

5. Example 1: use properties of square roots • Simplify the expression. a. b. ● c.

6. Rationalizing the denominator • To simplify an expression, you must eliminate any radical from the denominator.

7. Example 2: rationalize the denominator of a fraction

8. checkpoint

9. Example 3: solve a quadratic equation • Solve x2 + 1 = 13

10. checkpoint • x2 – 4 = 14 • x2 + 3 = 13

11. checkpoint • 3y2 = 24 • x2 + 2 = 26

12. Example: Solve a quadratic equation • 2(x – 5)2 = 12 • ½ (p + 4)2= 22

14. Homework:p. 258-260 #18-66 even, 75 - 78