5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots.

Slides:

Advertisements

Similar presentations

Roots of Real Numbers and Radical Expressions. Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any.

Advertisements

6. 1 roots and Radical Expressions 6

Splash Screen Inequalities Involving Absolute Values Lesson5-5.

7. Roots and Radical Expressions

EXAMPLE 1 Solve quadratic equations Solve the equation. a. 2x 2 = 8 SOLUTION a. 2x 2 = 8 Write original equation. x 2 = 4 Divide each side by 2. x = ±

Taking a Square Root to Solve an Equation. Solve: In order to solve for x, you have to UNDO the squared first (i.e. square root) What are the number(s)

Roots of Real Numbers and Radical Expressions. Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any.

Other types of Equations Polynomial Equations. Factoring Solve.

3.1 Evaluate nth Roots and Use Rational Exponents p. 166 What is a quick way to tell what kind of real roots you have? How do you write a radical in exponent.

Drill #37 Factor the following polynomials Simplify.

Algebra 2 Bellwork – 3/4/15.

Tidewater Community College

Recall that the radical symbol is used to indicate roots

7.1 nth Roots and Rational Exponents 3/1/2013. n th Root Ex. 3 2 = 9, then 3 is the square root of 9. If b 2 = a, then b is the square root of a. If b.

7.5 Graphs Radical Functions

Checking Factoring  The checking of factoring can be done with the calculator.  Graph the following expressions: 1.x 2 + 5x – 6 2.(x – 3)(x – 2) 3.(x.

Roots and Radicals. Radicals (also called roots) are directly related to exponents.

2.13 Warm Up x² - 2x + 15 = 0; 3 x² + 3x – 4 = 0; 1

6.1 Evaluate n th Roots & use Rational Exponents I.. Evaluating n th roots. A) n th roots are radicals to the n th index. B) Use the Church of Square Roots.

You should know or start to recognize these: 2 2 = 43 2 = 94 2 = = = 83 3 = = = = = = = = 323.

Algebra 2: Unit 8 Roots and Radicals. Radicals (also called roots) are directly related to exponents. Roots and Radicals.

Roots of Real Numbers.

Copyright © Cengage Learning. All rights reserved. Roots, Radical Expressions, and Radical Equations 8.

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Lesson 7-1: Radical Expressions Objectives Students will: Find square roots of numbers Find n-th root of numbers.

Chapter Rational Exponents.

+ 7.2 The Real nth Roots of a Number How many values in the domain of f are paired with the value in the range? That is, how many x values satisfy.

Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.

1 Algebra 2: Section 7.1 Nth Roots and Rational Exponents.

Notes Over 7.1 no real 4th roots Finding nth Roots

5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study.

Symbols Defn: is the positive (or principal) square root of a.

Warm up 1. Change into Scientific Notation 3,670,900,000 Use 3 significant figures 2. Compute: (6 x 10 2 ) x (4 x ) 3. Compute: (2 x 10 7 ) / (8.

Intermediate Algebra Chapter 7. Section 7.1 Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number.

Roots and Radical Expressions

Warm-up Simplify each expression

Warm-up Write as a rational exponent. Answers:. Notes P3, Day 3: Cube Roots and Rational Exponents Definition of the Principal nth Root of a Real Number.

Radical Expressions and Functions Find the n th root of a number. 2.Approximate roots using a calculator. 3.Simplify radical expressions. 4.Evaluate.

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Radical Expressions and Graphs.

Properties and Rules for Exponents Properties and Rules for Radicals

Algebra 2 Lesson 7-1 (Page 363) ALGEBRA 2 LESSON 7-1 Roots and Radical Expressions 7-1.

6.4 Completing the Square The Square Root Property.

7.1 Radicals and Radical Functions. Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a.

Roots of Real Numbers Definitions Simplifying Radicals

Section 5.5 Radicals and Roots. Def: For any real numbers a and b, if b = a 2 then a is a square root of b. So: But: Then a is a square root of b.

Nth Roots and Radicals Example 1: a is the nth root of b if and only if 2 is the third root of 8, since - 3 is the fifth root of - 243, since.

Aim: What is the complex number? Do Now: Solve for x: 1. x 2 – 1 = 0 2. x = 0 3. (x + 1) 2 = – 4 Homework: p.208 # 6,8,12,14,16,44,46,50.

Solving Radical Equations Steps Examples. Solving an Equation Containing a Radical  Steps  Isolate the radical  Take BOTH sides to the power.

Roots and Radicals. Radicals (also called roots) are directly related to exponents. Roots and Radicals.

1 Chapter 5, Section 5 Roots of Real Numbers. 2 Simplify Radicals Finding the square root of a number and squaring a number are inverse operations. To.

TOPIC 18.1 Radical Expressions

04 Evaluate nth Roots and Use Rational Exponents

6-1 Radical Functions & Rational Exponents

5.5 Roots of Real Numbers Definitions Simplifying Radicals

6.4 – nth Roots Day 1.

Roots of Real Numbers and Radical Expressions

Roots, Radicals, and Root Functions

Chapter 8 – Roots, Radicals and Rational Functions

Evaluate nth Roots and Use Rational Exponents

Roots of Real Numbers and Radical Expressions

nth Roots and Rational Exponents

Radicals and Radical Functions

9.2 Solving Quadratic Equations using square roots

Radicals and Radical Functions

Roots, Radicals, and Complex Numbers

Roots, Radicals, and Root Functions

6-7: Solving Radical Equations

nth Root & Rational Exponents

Performance Exam Tomorrow! 5% of Your Grade

Presentation transcript:

5.5 Roots of Real Numbers Squares Roots Nth Roots Principal Roots

Square Roots Since 4 2 = 16, then but (-4) 2 = 16. So the square root of 16 is 4 and -4? The Principal root is 4. The Principal root are always positive.

Cube roots 5 3 = 125, so Here are the parts of a root Square roots have index 2, which is not shown

N th root There are more roots then square or cubes.

How do I know if the answer is positive or negative For example: In case of numbers we take the principle root “5” When solve an equation x 2 = 25, you take the square root of both sides. Since Square roots are even “2”, the answer is 5 and -5

Even roots the answer have to come out positive Even roots Odd roots

Other Roots Some we will work with later in this class.

The ± symbol ± means positive and negative So Since x 2 is positive, it does not have to be in an absolute value

Simplify

How do you use your Calculator to find the values It depends on your calculator, normal it is function you can find with your shift button. We will have to find it on your calculator. Find the approximate value of

How do you use your Calculator to find the values It depends on your calculator, normal it is function you can find with your shift button. We will have to find it on your calculator. Find the approximate value of

Homework Page 248 – 249 #17 – 55 odd, 63

Homework Page 248 #16 – 58 even