Radicals 07/27/12lntaylor ©. Table of Contents Learning Objectives Parts of a Radical Simplifying Radicals Radical Expressions Estimating Radicals Practice.

Slides:

Advertisements

Similar presentations

Advertisements

Section P3 Radicals and Rational Exponents

Aim: How do we simplify radical expressions? Do Now: List at least 3 factors of: x 4.

11.1 Examples for Simplifying (EX: 1 of 4) Look for factors of 50 that are perfect square numbers. Take the square root of 25. Write it outside the radical.

Absolute Value 07/27/12lntaylor ©. Table of Contents Learning Objectives Absolute Value Number Line Simplifying Absolute Value Practice Simplifying Absolute.

11.1 Simplifying Radical Expressions

Discounts, Markups and Interest 07/30/12lntaylor ©

C ollege A lgebra Basic Algebraic Operations (Appendix A) L:5 1 Instructor: Eng. Ahmed Abo absa University of Palestine IT-College.

Radicals NCP 503: Work with numerical factors

Properties and Rules for Exponents Properties and Rules for Radicals

Objective: Add, subtract and multiplying radical expressions; re-write rational exponents in radical form. Essential Question: What rules apply for adding,

Exponents 07/24/12lntaylor ©. Table of Contents Learning Objectives Bases Exponents Adding Bases with exponents Subtracting Bases with exponents Multiplying.

Expressions Regents Review #1 Roslyn Middle School

10-1A Simplifying Radicals Algebra 1 Glencoe McGraw-HillLinda Stamper.

Percents 07/27/12lntaylor ©. Table of Contents Learning Objectives Straight Percent Change in Percent Percent/Fraction/Decimal Equivalents Table Practice.

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

Exponent Rules. Simplify each algebraic expression. Do NOT leave negative exponents.

R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.

Table of Contents Rational Exponents When a base is raised to a rational exponent of the form 1/n we use the following definition: The denominator of the.

Note that the denominator of the exponent becomes the index and the base becomes the radicand. Example Write an equivalent expression using radical.

Radical The whole equation is called the radical. C is the radicand, this must be the same as the other radicand to be able to add and subtract.

Simplifying Radicals Section 5.3. Radicals Definition Simplifying Adding/Subtracting Multiplying Dividing Rationalizing the denominator.

Radicals Simplify radical expressions using the properties of radicals

Chapter P Prerequisites: Fundamental Concepts of Algebra 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.3 Radicals and Rational Exponents.

Exponents and Radicals Objective: To review rules and properties of exponents and radicals.

EQ: How are properties of exponents used to simplify radicals? What is the process for adding and subtracting radicals?

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.

5-7 Rational Exponents Objectives Students will be able to:

Properties and Rules for Exponents Properties and Rules for Radicals

Rational Exponents Rules Examples Practice Problems.

Simplifying Radicals Binomial Conjugate:

Rational Exponents. Rational Exponent  “Rational” relates to fractions  Rational exponents mean having a fraction as an exponent. Each part of the fraction.

Rational Exponents March 2, 2015.

5-7 Rational Exponents Objectives Students will be able to:

Radicals (Square Roots). = 11 = 4 = 5 = 10 = 12 = 6 = 7 = 8 = 9 = 2.

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

Find the degree of the expressions: a)b)

Simplifying Radicals Algebra I Unit 1 D2. Perfect Squares

Rational (Fraction) Exponent Operations The same operations of when to multiply, add, subtract exponents apply with rational (fraction) exponents as did.

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.

Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. radical sign index radicand This symbol is the.

Algebra 1 Section 9.2 Simplify radical expressions

10-1C Simplifying Radicals

10-1A Simplifying Radicals

Simplifying Radical Expressions

Operations with Rational (Fraction) Exponents

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

Warm Up 1.) List all of the perfect squares up to The first three are done below. 1, 4, 9,… Using a calculator, evaluate which expressions are.

The exponent is most often used in the power of monomials.

Simplifying Square Root Expressions

12.1 Operations with Radicals

Properties and Rules for Exponents Properties and Rules for Radicals

10-1C Simplifying Radicals

Unit 1 Algebra 2 CP Radicals.

9.1 Properties of Radicals

Exponent Rules.

1.4 Rational Exponents.

5.7 Rational Exponents 1 Rules 2 Examples 3 Practice Problems.

Adding & Subtracting Radical Expressions

Simplifying Square Roots

5.2 Properties of Rational Exponents and Radicals

Essential Question: How do we simplify radicals?

Square Roots and Simplifying Radicals

Simplifying Radicals.

P.3 Radicals and Rational Exponents

Presentation transcript:

Radicals 07/27/12lntaylor ©

Table of Contents Learning Objectives Parts of a Radical Simplifying Radicals Radical Expressions Estimating Radicals Practice 07/27/12lntaylor ©

LO1: LO2: Define and differentiate radicals, radicands and root index Estimate and simplify radical expressions 07/27/12lntaylor © TOC Learning Objectives

PK1:Knowledge of exponent operations 07/27/12lntaylor © TOC Previous Knowledge

Def1: Def2: 07/27/12lntaylor © TOC Parts of a Radical Expression (Definitions) Def3:

07/27/12lntaylor © TOC Simplifying Radicals Step1:To simplify a radical you must first know your perfect squares Step2:Only then will you understand the square roots Step3:Memorize the following charts (perfect squares and square roots)

07/27/12 lntaylor © TOC SquaresEquivalents > 4 > > > > > > 64 > 81 > 100 > > > > > clear answers

07/27/12 lntaylor © TOC Square RootsEquivalents > 2 > > > > > > 8 > 9 > 10 > > > > > clear answers

07/27/12lntaylor © TOC Square RootsEquivalents > 2 > > > > > > 8 > 9 > 10 > > > note Do you see that the square root of a number squared is that number? clear answers

Step1: Step2: This radicand (24) is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of 24? 07/27/12lntaylor © TOC Step3:Hint: Only one combination includes a perfect square Rewrite the problem with 2 radicals Step4:Simplify (reduce) the radical containing the perfect square Leave the other alone Step5:This is your final answer =2(12) 3(8) 4(6)

07/26/12lntaylor © TOC

Step1: Step2: This radicand (28) is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of 28? 07/27/12lntaylor © TOC Step3:Hint: Only one combination includes a perfect square Rewrite the problem with 2 radicals Step4:Simplify (reduce) the radical containing the perfect square Leave the other alone Step5:This is your final answer =2(14) 3(not a whole number) 4(7)

07/26/12lntaylor © TOC

Step1: Step2: This radicand is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of the radicand? 07/27/12lntaylor © TOC Step3:Hint: make sure you factor out all perfect squares! Rewrite the problem with 3 radicals Step4:Simplify (reduce) any radicals containing the perfect squares Leave the other alone Step5:This is your final answer =9(8) 9(4)(2)

07/26/12lntaylor © TOC

Step1: Step2: This radicand is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of the radicand? 07/27/12lntaylor © TOC Step3:Hint: make sure you factor out all perfect squares! Rewrite the problem with 3 radicals Step4:Simplify (reduce) any radicals containing the perfect squares Leave the other alone Step5:This is your final answer =25(27) 25(9)(3)

07/26/12lntaylor © TOC

Step1: Step2: This radicand is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of the radicand? 07/27/12lntaylor © TOC Step3:Hint: make sure you factor out all perfect squares! Rewrite the problem with radicals Step4:Simplify (reduce) any radicals containing the perfect squares Leave the other alone Step5:This is your final answer =16(10)

07/27/12lntaylor © TOC Radical Expressions Step1:To simplify radical expressions you must first understand exponents Step2:Only then will you understand the radical expressions Step3:Memorize the following charts (square root exponents)

07/27/12lntaylor © TOC Square RootsEquivalents > 2x > > > > > > > 2xy > > > note Do you see that the square root of an even exponent is half the exponent; the square root of an odd exponent puts half the exponent outside the radical and leaves an exponent of 1 under the radical? clear answers

07/27/12lntaylor © TOC Radical Expressions Note:If you understood the preceding chart then you are ready to go on!

07/26/12lntaylor © TOC

Step1: Step2: To do these properly you must “unpack” each part of the expression There are 2 parts here! Start by factoring each radicand 07/27/12lntaylor © TOC Step3:Hint: make sure you have factored out all perfect squares! Simplify the problem Step4:This is your final answer 2x(3y) 6xy

07/26/12lntaylor © TOC

Step1: Step2: To do these properly you must “unpack” each part of the expression There are 2 parts here! Start by factoring each radicand 07/27/12lntaylor © TOC Step3:Hint: make sure you have factored out all perfect squares! Simplify the problem Step4:This is your final answer (9y)

07/26/12lntaylor © TOC

Step1: Step2: To do these properly you must “unpack” each part of the expression There are 2 parts here! Start by factoring the perfect squares out of each radicand 07/27/12lntaylor © TOC Step3:Hint: make sure you have factored out all perfect squares! Rewrite the problem Cancel any terms Step4:This is your final answer

07/26/12lntaylor © TOC

Step1: Step2: To do these properly you must “unpack” each part of the expression There are 2 parts here! Start by factoring the perfect squares out of each radicand 07/27/12lntaylor © TOC Step3:Hint: make sure you have factored out all perfect squares! Rewrite the problem Cancel any terms Step4:This is your final answer

07/27/12lntaylor © TOC Estimating Radicals

Step1: Step2: Estimating a radical is not difficult First figure out which two perfect squares it lies between Factor the perfect squares onto a number line 07/27/12lntaylor © TOC Step3:Find the range between the perfect square radicands(64 – 49) This becomes the denominator Subtract the middle radicand (60) from the lower radicand (49) This becomes the numerator Estimate the decimal equivalent of the fraction Step4: – 49 = 15 __ – 49 = ≈

07/26/12lntaylor © TOC

Step1: Step2: Estimating a radical is not difficult First figure out which two perfect squares it lies between Factor the perfect squares onto a number line 07/27/12lntaylor © TOC Step3:Find the range between the perfect square radicands(100 – 86) This becomes the denominator Subtract the middle radicand (86) from the lower radicand (81) This becomes the numerator Estimate the decimal equivalent of the fraction Step4: – 81 = 19 __ – 81 = 5 5 ≈

07/26/12lntaylor © TOC

Step1: Step2: Estimating a radical is not difficult First figure out which two perfect squares it lies between Factor the perfect squares onto a number line 07/27/12lntaylor © TOC Step3:Find the range between the perfect square radicands This becomes the denominator Subtract the middle radicand from the lower radicand This becomes the numerator Estimate the decimal equivalent of the fraction Step4: – 196 = 29 __ – 196 = 4 4 ≈

07/27/12lntaylor © TOC Practice

07/27/12lntaylor © TOC ProblemAnswer > ≈ 5.78 > > > > > ≈ > ≈ 4.44 > > clear answers