Download presentation

Presentation is loading. Please wait.

Published byTracy Higgins Modified over 6 years ago

1
Chapter 8 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2
Evaluating Roots Find square roots. Decide whether a given root is rational, irrational, or not a real number. Find decimal approximations for irrational square roots. Use the Pythagorean formula. Use the distance formula. Find cube, fourth, and other roots. 1 1 4 4 3 3 2 2 6 6 5 5 8.18.1

3
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Find square roots. Slide 8.1 - 3

4
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find square roots. When squaring a number, multiply the number by itself. To find the square root of a number, find a number that when multiplied by itself, results in the given number. The number a is called a square root of the number a 2. Slide 8.1 - 4

5
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The positive or principal square root of a number is written with the symbol. Find square roots. (cont’d) Slide 8.1 - 5 Radical Sign Radicand The symbol, is called a radical sign, always represents the positive square root (except that ). The number inside the radical sign is called the radicand, and the entire expression—radical sign and radicand—is called a radical. The symbol – is used for the negative square root of a number.

6
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find square roots. (cont’d) Slide 8.1 - 6 The statement is incorrect. It says, in part, that a positive number equals a negative number.

7
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1 Find all square roots of 64. Solution: Finding All Square Roots of a Number Slide 8.1 - 7

8
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find each square root. EXAMPLE 2 Solution: Finding Square Roots Slide 8.1 - 8

9
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Squaring Radical Expressions Slide 8.1 - 9 Find the square of each radical expression. Solution:

10
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Decide whether a given root is rational, irrational, or not a real number. Slide 8.1 - 10

11
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Deciding whether a given root is rational, irrational, or not a real number. Slide 8.1 - 11 All numbers with square roots that are rational are called perfect squares. Perfect SquaresRational Square Roots 25 144 A number that is not a perfect square has a square root that is irrational. Many square roots of integers are irrational. Not every number has a real number square root. The square of a real number can never be negative. Therefore, is not a real number.

12
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Identifying Types of Square Roots Slide 8.1 - 12 Tell whether each square root is rational, irrational, or not a real number. Solution: Not all irrational numbers are square roots of integers. For example (approx. 3.14159) is a irrational number that is not an square root of an integer.

13
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Slide 8.1 - 13 Find decimal approximations for irrational square roots.

14
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find decimal approximations for irrational square roots. Slide 8.1 - 14 A calculator can be used to find a decimal approximation even if a number is irrational.

15
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 Approximating Irrational Square Roots Slide 8.1 - 15 Find a decimal approximation for each square root. Round answers to the nearest thousandth. Solution:

16
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4 Objective 4 Slide 8.1 - 16 Use the Pythagorean formula.

17
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Many applications of square roots require the use of the Pythagorean formula. If c is the length of the hypotenuse of a right triangle, and a and b are the lengths of the two legs, then Slide 8.1 - 17 Use the Pythagorean formula. Be careful not to make the common mistake thinking that equals.

18
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 6 Using the Pythagorean Formula Slide 8.1 - 18 Find the length of the unknown side in each right triangle. Give any decimal approximations to the nearest thousandth. 11 8 ? Solution:

19
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 7 Using the Pythagorean Formula to Solve an Application Slide 8.1 - 19 A rectangle has dimensions of 5 ft by 12 ft. Find the length of its diagonal. 5 ft 12 ft Solution:

20
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5 Objective 5 Use the distance formula. Slide 8.1 - 20

21
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8.1 - 21 Use the distance formula. The distance between the points and is

22
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 8 Using the Distance Formula Slide 8.1 - 22 Find the distance between and. Solution:

23
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 6 Objective 6 Find cube, fourth, and other roots. Slide 8.1 - 23

24
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Finding the square root of a number is the inverse of squaring a number. In a similar way, there are inverses to finding the cube of a number or to finding the fourth or greater power of a number. The nth root of a is written Find cube, fourth, and other roots. Slide 8.1 - 24 Radical sign Index Radicand In, the number n is the index or order of the radical. It can be helpful to complete and keep a list to refer to of third and fourth powers from 1-10.

25
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find each cube root. Solution: EXAMPLE 9 Finding Cube Roots Slide 8.1 - 25

26
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 10 Finding Other Roots Slide 8.1 - 26 Find each root. Solution:

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google