1. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 4.6 Square Roots and The Pythagorean Theorem

2. 22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Finding Square Roots Square Root of a Number A square root of a number a is a number b whose square is a. We use the radical sign to name square roots. In symbols,

3. 33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Find each square root. a. b. c.

4. 44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Approximate each square root to the nearest thousandth. a. b. c.

5. 55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using the Pythagorean Theorem Pythagorean Theorem In any right triangle, (leg) 2 + (other leg) 2 = (hypotenuse) 2 hypotenuse leg

6. 66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using the Pythagorean Theorem Finding an Unknown Length of a Right Triangle

7. 77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the length of the hypotenuse of the given right triangle. 48 m 22 m The hypotenuse is approximately 53 meters long.

8. 88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the length of the leg of the given right triangle. 3 yd 9 yd The leg is approximately 8 yards long.