Lesson Cube Roots and More* (Basic Algebra YouTube Video of Dr. Rapalje)

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About rapaljer: Retired Professor of Mathematics from Seminole State College of Florida after 36 years.

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This video is an explanation about simplifying cube roots with a few fourth and fifth roots  from one of my Basic Algebra classes (circa 1994). This video will be helpful to students in Basic or Intermediate Algebra.

In the last section, it was necessary to KNOW (memorize by heart!) the PERFECT SQUARES:
{{{1^2=1}}}   {{{2^2=4}}}   {{{3^2=9}}}   {{{4^2=16}}}   {{{5^2=25}}}   {{{6^2=36}}} {{{7^2=49}}}   {{{8^2=64}}}   {{{9^2=81}}}   {{{10^2=100}}}   {{{11^2=121}}}   {{{12^2=144}}}   {{{13^2=169}}}

These are the critical numbers to KNOW and recognize were:  1,  4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169.

Now, you need to know the following perfect powers:

{{{1^3=1}}}   {{{1^4=1}}}   {{{1^5=1}}}

{{{2^3=8}}}   {{{2^4=16}}}   {{{2^5=32}}}

{{{3^3=27}}}   {{{3^4=81}}}

{{{4^3=64}}}

{{{5^3=125}}}

The perfect cubes are 1, 8, 27, 125.

The perfect 4th powers are 1, 16, 81.

The perfect 5th powers are 1 and 32.

If you recognize these perfect cubes (8, 27, 64, and 125), you can do cube roots!

If you recognize these perfect fourth powers (16 and 81), you can do fourth roots!

The only fifth power small enough to be used here is 32, so fifth roots almost always have to do with 32!!!

Unfortunately, in this era of teaching the calculators of today were not available, nor was I aware of the wonderful ability to check your answers with a calculator.  
You can use a calculator to calculate the decimal approximation of the exercise and the answer you get.  If these values do NOT agree, you have an error to find--BEFORE you turn your test or homework in!!

For explanations, examples, and exercises for ALL topics from Basic, Intermediate, and College Algebra, and 
Practice Tests for ALL levels of math from Pre-Algebra to Calculus III and Differential Equations with DETAILED SOLUTIONS, please see my website at www.mathinlivingcolor.com!!