Simplifying Radicals Section 10-2. Objectives Simplify radicals involving products Simplify radicals involving quotients.

Slides:

Advertisements

Similar presentations

Warm Up Simplify each expression

Advertisements

1-3 Square Roots Warm Up Lesson Presentation Lesson Quiz

Section P3 Radicals and Rational Exponents

Multiplying and Dividing Radial Expressions 11-8

11-1: Simplifying Radicals

7.1 – Radicals Radical Expressions

Section 10.3 – 10.4 Multiplying and Dividing Radical Expressions.

Multiplying and Dividing Radial Expressions 11-8

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec

Simplifying Radicals SPI Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands.

243 = 81 • 3 81 is a perfect square and a factor of 243.

Find the Square Root: 1) 3) 2) 4)

WARM UP POWER OF A PRODUCT Simplify the expression. 1.(3x) 4 2.(-5x) 3 3.(xy) 6 4.(8xy) 2 4.

3.6 Solving Quadratic Equations

Prentice Hall Lesson How do you simplify a radical expression

Simplifying Radical Expressions Chapter 10 Section 1 Kalie Stallard.

243 = 81 • 3 81 is a perfect square and a factor of 243.

Lesson 10-1 Warm-Up.

Simplify Radical Expressions. EQs…  How do we simplify algebraic and numeric expressions involving square root?  How do we perform operations with square.

Including Rationalizing The Denominators. Warm Up Simplify each expression

6.3 Binomial Radical Expressions P You can only use this property if the indexes AND the radicands are the same. This is just combining like terms.

6.3 Simplifying Radical Expressions In this section, we assume that all variables are positive.

Simplify Radical Expressions Warm-up: Recall how to estimate the square root of a number that is not a perfect square. 1.) The is between the perfect square.

Complete each equation. 1. a 3 = a2 • a 2. b 7 = b6 • b

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

Powers, Roots, & Radicals OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.

SIMPLIFYING RADICAL EXPRESSIONS

Conjugate of Denominator

Copyright © Cengage Learning. All rights reserved. 8 Radical Functions.

Advanced Algebra Notes Section 4.5: Simplifying Radicals (A) A number r is a _____________ of a number x if. The number r is a factor that is used twice.

Lesson 1 MI/Vocab radical expression radicand rationalizing the denominator conjugate Simplify radical expression using the Product Property of Square.

Holt Algebra Multiplying and Dividing Radical Expressions Warm Up(On Separate Sheet) Simplify each expression

Holt Algebra Multiplying and Dividing Radical Expressions Warm Up Simplify each expression

3.4 Simplify Radical Expressions PRODUCT PROPERTY OF RADICALS Words The square root of a product equals the _______ of the ______ ______ of the factors.

7.4 Dividing Radical Expressions  Quotient Rules for Radicals  Simplifying Radical Expressions  Rationalizing Denominators, Part

 A radical expression is an expression with a square root  A radicand is the expression under the square root sign  We can NEVER have a radical in the.

7.5 Operations with Radical Expressions. Review of Properties of Radicals Product Property If all parts of the radicand are positive- separate each part.

 Simplify then perform the operations indicated….

Radicals. Parts of a Radical Radical Symbol: the symbol √ or indicating extraction of a root of the quantity that follows it Radicand: the quantity under.

Warm Up Simplify each expression

Multiplying and Dividing Radial Expressions 11-8

Section 7.5 Expressions Containing Several Radical Terms

Simplifying Radicals Section 10-2 Part 2.

Multiplying and Dividing Radial Expressions 11-8

Multiplying & Dividing Radical Expressions

6.2 Multiplying and Dividing Radical Expressions

Multiplying Radicals.

Solve Quadratic Equations by Finding Square Roots

Simplifying Square Roots

Use Properties of Radicals to simplify radicals.

Do-Now: Simplify (using calculator)

7.2 – Rational Exponents The value of the numerator represents the power of the radicand. The value of the denominator represents the index or root of.

Simplifying Radical Expressions

Multiplying and Dividing Radial Expressions 11-8

Unit 3B Radical Expressions and Rational Exponents

Warm up Simplify

Objectives Rewrite radical expressions by using rational exponents.

Warm Up Simplify each expression

Simplify Radical Expressions

Complete each equation. 1. a 3 = a2 • a 2. b 7 = b6 • b

Algebra 1 Section 11.4.

5.2 Properties of Rational Exponents and Radicals

1.2 Multiply and Divide Radicals

The radicand can have no perfect square factors (except 1)

Multiplying and Dividing Rational Expressions

10-1 Simplifying Radicals

Chapter 8 Section 4.

ALGEBRA I - SECTION 10-2 (Simplifying Radicals)

Dividing Radical Expressions

Roots, Radicals, and Root Functions

Presentation transcript:

Simplifying Radicals Section 10-2

Objectives Simplify radicals involving products Simplify radicals involving quotients

Radical expressions Contain a radical Index = 2 if not specified otherwise radical radicand

Perfect squares The way we simplify radicals is by removing perfect square factors from the radicand, such as…. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, etc

Multiplication Property of Square Roots We will use this property to simplify radical expressions.

Simplify = is a perfect square and a factor of 243. = 81 3Use the Multiplication Property of Square Roots. = 9 3Simplify 81.

Your turn

Simplify 28x 7. 28x 7 = 4x 6 7x 4x 6 is a perfect square and a factor of 28x 7. = 4x 6 7xUse the Multiplication Property of Square Roots. = 2x 3 7x Simplify 4x 6.

Your turn

Simplify each radical expression. a = 12 32Use the Multiplication Property of Square Roots. = 384Simplify under the radical. = is a perfect square and a factor of 384. = 64 6Use the Multiplication Property of Square Roots. = 8 6Simplify 64.

(continued) b. 7 5x 3 8x = 42x 10Simplify. = 21 2x 10Simplify 4x 2. = 21 4x 2 10 Use the Multiplication Property of Square Roots. = 21 4x 2 104x 2 is a perfect square and a factor of 40x x 3 8x = 21 40x 2 Multiply the whole numbers and use the Multiplication Property of Square Roots.

Your turn

Suppose you are looking out a fourth floor window 54 ft above the ground. Use the formula d = 1.5h to estimate the distance you can see to the horizon. d = 1.5h The distance you can see is 9 miles. = 9Simplify 81. = 81Multiply. = Substitute 54 for h.

Your turn Suppose you are looking out a second floor window 25 ft above the ground. Find the distance you can see to the horizon. Round your answer to the nearest mile.

Division Property of Square Roots

Simplify each radical expression. =Simplify a b. 49 x 4 7 x 2 =Simplify 49 and x 4. =Use the Division Property of Square Roots =Use the Division Property of Square Roots. 49 x 4 49 x 4

Your turn

= 12Divide = 4 34 is a perfect square and a factor of 12. a Simplify each radical expression. = 4 3Use the Multiplication Property of Square Roots. = 2 3Simplify 4.

b. 75x 5 48x =Divide the numerator and denominator by 3x. 75x 5 48x 25x 4 16 =Use the Division Property of Square Roots. 25x 4 16 (continued) = Use the Multiplication Property of Square Roots. 25 x 4 16 = Simplify 25, x 4, and 16. 5x 2 4

Your turn

Rationalizing the denominator A process used to force a radicand in the denominator to be a perfect square by multiplying both the numerator & denominator by the same radical expression.

= Multiply by to make the denominator a perfect square. Simplify each radical expression. a. 3 7 = Simplify = Use the Multiplication Property of Square Roots

= Simplify 36x 4. 33x 6x 2 (continued) b x 3 Simplify the radical expression. = Multiply by to make the denominator a perfect square. 3x 11 12x x 3 = Use the Multiplication Property of Square Roots. 33x 36x 4

Your turn

A radical is simplified when…