1. 9.1 – Finding Square Roots

2. We know how to find the square of a number: 3 2 = (-3) 2 =

3. Today we are going to learn how to: Evaluate and approximate square roots The reverse of squaring a number

4. Square Root of a Number If b 2 = a, then b is a square root of a. If 3 2 = 9, then 3 is a square root of 9

5. All positive real numbers have 2 square roots: Positive Square Root: Negative Square Root: Square roots are written with a radical symbol √ The number inside the radical symbol is called the radicand

6. Meaning Positive Square Root Negative Square Root The positive and negative square roots Symbol √ -√ ±√ Example √9 = 3-√9 = -3 ±√9 = ±3 = +3 or -3

7. Example 1 Evaluate the expression √81 -√81 -√0 ±√0.0016 √-9

8. Perfect Squares – Numbers whose square roots are integers or quotients of integers. Irrational Number – number that cannot be written as the quotient of two integers Must be written using the radical symbol or approximated √7

9. Example 2 Evaluate the expression. Use a calculator if necessary. -√36 √1.21 -√0.04 √8

10. Radical expression - involves square roots (or radicals). If the ± symbol is before the radical, the expression represents 2 different numbers The square root symbol is a group symbol. Operations inside must be performed first

11. Example 3 Evaluate √(b 2 – 4ac) for a = 7, b = 8, and c = 1.

12. Example 4 Evaluate 1 ± 2√6 to the nearest hundredth. 4

13. HOMEWORK Page 507 #24 – 52 even