1. Section 5.2 Multiplying, Dividing, and Rationalizing Radicals:

2. 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

3. 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
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4. Practice: Multiply the radicals
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6. Example 3: Expand and Simplify.

8. 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
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9. Ex: Rationalize the following
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10. 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
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11. Ex: Simplify the following by rationalizing the denominator
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12. 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
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13. Rationalize:

14. Assignment 5.2