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Kansas State Polytechnic

R.8 Radicals

1: The Basics of Simplifying Radicals

This video covers:
*Review of what are radicals/roots from R.1 Roots Video #4
*Review of how radicals/roots are the opposites of exponents
*How radicals simplify when there are negatives involved

Examples:
Basic Radical Examples

 


 2: Simplifying Radicals with Variables (That Come Out Evenly), Radical Properties

This video covers:
*How to simplify radicals with variables (letters) in them
*The full details of how the radicals simplify and the shorter process to simplify them
*The properties associated with radicals
*How to handle roots with variables and negatives
*When you can and cannot combine and separate roots

Examples:
Variable Radical Examples

 


3: Simplifying Radicals That Don't Simplify Evenly - Good and Bad Pie (Part 1)

This video covers:
*How baking a pie can help you understand how to simplify radicals
*The full details of how the radicals simplify
*Why knowing squares/cubes/etc. can save you a lot of time
*Why you should use the largest square/cube/etc should be used in your good pie

Examples:
Pie Radical Examples

 


4: Simplifying Radicals That Don't Simplify Evenly - Good and Bad Pie (Part 2) - Examples

This video covers:
*Review of what all goes into your good pie and your bad pie
*Why knowing squares/cubes/etc. can save you a lot of time
*When to actually simplify your good pie
*This simple mistake of leaving off the root number

Examples:
Pie Radical Examples

 


5: Multiplying and Dividing Radical Expressions

 This video covers:
*How to multiply and divide radicals using the properties learned in video #2
*Review of how to simplify radicals using good pie and bad pie
*When simplifying radicals is not the best first step
*A suggestion to review how to multiply and divide identical bases with exponents R.4 Video #2 Exponent Properties 1 and 2

Examples:
Multiplying and Dividing Radical Examples

 


 6: Adding and Subtracting Radical Expressions

This video covers:
*Review of like terms
*How to add and subtract radicals
*Review of how to simplify radicals using good pie and bad pie
*Reminder to copy all the details from step to step
*

Examples:
Adding and Subtracting Radical Examples

 


 7: Multiplying Polynomial Style Type of Radicals

This video covers:
*A hint to simplify identical square roots
*Review of multiplying polynomials R.5 Video #5 and #6
*Review of what not to do to kill puppies during math

Examples:
Multiplying Polynomial Style Radical Examples

 


 8: Rationalizing the Denominator - Simple Examples

This video covers:
*Review of how to simplify fractions
*How to rationalize the denominator when there isn't any addition or subtraction involved

Examples:
Easy Rationalizing the Denominator Examples

 


9: Rationalizing the Denominator with Addition or Subtraction

This video covers:
*How to rationalize the denominator when there is addition or subtraction in the denominator
*Review of the vocabulary word: conjugate
*How using the conjugate helps us to rationalize the denominator
*Reminder to simplify completely

Examples:
Hard Rationalizing the Denominator Examples

 


10: Rational Exponents

This video covers: 
*Review of integer exponents
*What is a rational exponent
*Converting rational exponents to radical notations and simplifying
*Converting radicals/roots to rational exponents and simplifying

Examples:
Rational Exponents Examples