LESSON 2 MULTIPLYING DIVIDING AND RATIONALIZING RADICALS In

LESSON 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 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

PRACTICE: RATIONALIZE

FOIL: EXPAND THE FOLLOWING

III) RATIONALIZING WITH CONJUGATES When the denominator is a binomial with a radical, 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 Note: We only multiply by the conjugate of the denominator, b/c we only want to rid the bottom of radicals!!! © Copyright all rights reserved to Homework depot: www. BCMath. ca

Ex: Simplify the following by rationalizing the denominator Note: Multiply the top & bottom of the original fraction by the “conjugate” of 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: