Rationalizing.

Slides:

Advertisements

Similar presentations

Advertisements

To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator.

There is an agreement in mathematics that we don’t leave a radical in the denominator of a fraction.

Simplifying, Multiplying, & Rationalizing Radicals

There is an agreement in mathematics that we don’t leave a radical in the denominator of a fraction.

It’s a Dog’s World! Multiplying and Dividing Square Roots.

EXAMPLE 1 Writing Equivalent Fractions. EXAMPLE 1 Writing Equivalent Fractions Write two fractions that are equivalent to. Writing Equivalent Fractions.

Examples for Rationalizing the Denominator Examples It is improper for a fraction to have a radical in its denominator. To remove the radical we “rationalize.

Changing Percents to a Fraction #3 To change a percent to a fraction you need to first write the numerator over 100. Next simplify the fraction.

1.5 Solving Quadratic Equations by Finding Square Roots

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Developmental.

5.3 Solving Quadratic Equations by Finding Square Roots (p. 264) How do you simplify radicals? What are the steps to rationalize a denominator? How many.

Notes Over 9.4 Simplifying a Rational Expression Simplify the expression if possible. Rational Expression A fraction whose numerator and denominator are.

Chapter 9: Rational Expressions Section 9-1: Multiplying and Dividing Rationals 1.A Rational Expression is a ratio of two polynomial expressions. (fraction)

 Multiply rational expressions.  Use the same properties to multiply and divide rational expressions as you would with numerical fractions.

Multiplication of Fractions with Mixed Numbers. Copyright © 2000 by Monica Yuskaitis How to Find a Fraction of a Mixed Number The first thing to remember.

Rationalizing the Denominator. Essential Question How do I get a radical out of the denominator of a fraction?

Factor each of these– put the answers on a new sheet of paper on which you will start section A.3…

5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.

Multiplication of Fractions with Mixed Numbers

By: Ruthie Covington. Directions First you find two fractions. If you have a mixed number, then you multiply the whole number by the denominator.

Simplifying Radicals. Perfect Squares

Dividing Fractions. A. Review  Examples of fractions.

Jim Smith JCHS. Perfect Squares If You Multiply A Number By It’s Self, You Get A Perfect Square 1x1 = 1 2x2 = 4 3x3 = 9 1, 4, 9, 16, 25, 36, 49, 64, 81,

Ch 8: Exponents D) Rational Exponents

MULTIPLYING MIXED NUMBERS OBJECTIVE: I will multiply mixed numbers (using cross canceling to simplify) VOCABULARY: MIXED NUMBER – a number made up of a.

To divide radicals: divide the coefficients divide the radicands if possible rationalize the denominator so that no radical remains in the denominator.

Conjugate: Value or that is multiplied to a radical expression That clears the radical. Rationalizing: Removing a radical expression from the denominator.

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

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

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.

Multiplying Fractions. There are 5 types of problems… 1) Fraction x Fraction 2) Whole number x Fraction 3) Mixed number x Mixed number 4) Mixed number.

Date: Topic: Simplifying Radicals (9.1) Warm-up:Find the square root Simplify the radical:

 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.

Fractional Expressions Section 1.4. Objectives Simplify fractional expressions. Multiply and divide fractional expressions. Add and subtract fractional.

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

A or of radicals can be simplified using the following rules. 1. Simplify each in the sum. 2. Then, combine radical terms containing the same and. sumdifference.

Section 5-4 The Irrational Numbers Objectives: Define irrational numbers Simplify radicals Add, subtract, multiply, and divide square roots Rationalize.

1-6 Radicals (Day 1) and Rational Exponents (Day 2)

Multiplying Fractions and Mixed Numbers

Do Now: Multiply the expression. Simplify the result.

Simplifying Rational Expressions. Simplifying Rational Expressions.

Math 71B 7.5 – Multiplying with More Than One Term and Rationalizing Denominators.

Multiplying Fractions and Mixed Numbers

Multiplying and Dividing Rational Expressions

Radical Operations Unit 4-3.

Change each Mixed Number to an Improper Fraction.

Multiplying and Dividing Rational Expressions

Simplify Complex Rational Expressions

Rationalizing Roots Objective:

Simplifying Complex Rational Expressions

Warm Up = = = = = = = =.

Algebra JEOPARDY Jeopardy!.

Simplifying Radicals.

Simplifying rational expressions

Simplify Radicals.

Which fraction is the same as ?

Section 7.1 Radical Expressions

Section 7.2 Rational Exponents

Dividing Radicals To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains.

11.1b Rationalizing Denominators

Section 2.6 Rationalizing Radicals

Lesson #3: Dividing with Radicals (For use with Sections 7-2 & 7-3)

Dividing Radical Expressions

Unit 3: Rational Expressions Dr. Shildneck September 2014

Section 7.2 Adding and Subtracting Rational Expressions.

Presentation transcript:

Rationalizing

that we don’t leave a radical There is an agreement in mathematics that we don’t leave a radical in the denominator of a fraction.

So how do we change the denominator of a fraction? (Without changing the value of the fraction, of course.)

The same way we change the denominator of any fraction! (Without changing the value of the fraction, of course.)

We multiply the denominator and the numerator by the same number.

By what number can we multiply to change it to a rational number?

The answer is . . . . . . by itself!

Remember, is the number we square to get n. So when we square it, we’d better get n.

In our fraction, to get the radical out of the denominator, we can multiply numerator and denominator by .

In our fraction, to get the radical out of the denominator, we can multiply numerator and denominator by .

Because we are changing the denominator to a rational number, we call this process rationalizing.

Rationalize the denominator: (Don’t forget to simplify)

Rationalize the denominator:

Directions: Complete these on a sheet of paper Directions: Complete these on a sheet of paper. Label your paper “Rationalizing the Denominator” and place in your classwork folder. You should also have your Name, date, and section in your top right hand corner.