1. Section 5.1 Basics with Radicals

2. I) Review: Squares and Cubes
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3. II) What are Radicals
A radical is a symbol that involves the square root or nth root of a number
A radical can also be viewed as a fractional exponent
Entire Radicals vs Mixed Radicals

4. III) Properties of Radicals
The nth root of a radical indicates the number of terms required to simplify a radical
Suppose the nth root was “5”, you will need five factors to cancel out the root
If you have more factors than the roots, then take out the factors that can be simplified and then leave the remaining factors inside the radical

5. Ex: Simplify each entire radical to a mixed radical
A cube root means that you need a perfect cube
to take it out of the root
If you have too many factors,
combine three together and leave the rest

6. Practice: Simplify and convert to a mixed radical:

7. IV) Converting Mixed Radicals to Entire Radicals
When converting from mixed radicals back to entire radicals, each factor outside will go back into the radicals to the nth power

8. Ex: Arrange the following from least to greatest:
Convert each mixed radical to complete radicals
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9. IV) Adding & Subtracting Radicals
You can only add two polynomials if they are like terms
Likewise, you can only add or subtract two radicals if they are “like radicals”
Simplify a radical if the number inside the radical sign becomes the same
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10. Simplify the following:
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11. HW: assignment 5.1