Section 5.2 Multiplying, Dividing, and Rationalizing Radicals:

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Presentation transcript:

Section 5.2 Multiplying, Dividing, and Rationalizing Radicals:

In this section, you will learn three basic operations with radicals Multiplying radicals What’s outside stays outside and what’s inside stays inside When two equal radicals multiply each other, the radical sign disappears Dividing radicals Simplify what’s outside the radical and then what’s inside the radical Rationalizing radicals If the denominator is a monomial, then multiply the top and bottom by the radical in the denominator This eliminates the radical in the bottom If the denominator is a binomial, then multiply the top and bottom by the conjugate of the denominator

I) Multiplying Radicals The product of two similar radicals will become a whole number When multiplying radicals, numbers outside stay outside, numbers inside stay inside Ex: Simplify the following © Copyright all rights reserved to Homework depot: www.BCMath.ca

Practice: Multiply the radicals © Copyright all rights reserved to Homework depot: www.BCMath.ca

Example 3: Expand and Simplify.

II) Dividing Radicals: When dividing radicals, simplify by dividing the numbers outside the radical together, and then the numbers inside. Never leave a radical in the denominator. Rationalize by multiplying both the numerator and denominator be the radical in the denominator © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Rationalize the following © Copyright all rights reserved to Homework depot: www.BCMath.ca

III) Rationalizing with Conjugates When we have a fraction with a radical in the denominator, we want to rationalize it by multiplying both the top and bottom by the conjugate of the denominator Multiplying a binomial with it’s conjugate will eliminate all the radicals © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Simplify the following by rationalizing the denominator © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Simplify and Rationalize Rationalize each fraction separately Find the LCD so that you can add the fractions Combine the numerators (tops) when the bottom are the same © Copyright all rights reserved to Homework depot: www.BCMath.ca

Rationalize:

Assignment 5.2