Question 386903: how do you slimpify the 3rd root of -216?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The first thing to do (if you don't have a calculator that will take cube roots!) is recognize that 216 is a perfect cube. Since this is a cube root, by trial and error, make a list of some perfect cubes. Start with 1^3 =1, 2^3=8, 3^3=27, and keep going (or use a regular calculator!!) until you get to 6^3 = 216.
This means that the cube root of 216 is 6, since 6^3=216.
Next, deal with the negative.
Cube root of -216 = -6, since (-6)^3=-216. However, this thing about NEGATIVES will ONLY work for CUBE ROOT, FIFTH ROOT, etc. (Odd powers only!)
If you need help with other cube roots, you may want to see my own website, but in what I have posted here, I did NOT do very much with cube roots of NEGATIVE numbers. To see my website click on my tutor name "rapaljer" anywhere in algebra.com. Look for the link to my website there. From my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", click on "Basic Algebra," and then "Chapter 5," which is my chapter on Square Roots and other Radicals. Look in "Section 5.02" which is called "Cube Roots and Higher". For a higher level of explanation, please take a look at my "Intermediate Algebra" and look in "Chapter 3" for topics on radicals. See also the solutions of many of these exercises in the "MATH IN LIVING COLOR" pages, where the problems are solved in COLOR. My own students and others have been unanimous in telling me that my own explanations are easier to understand than the expensive textbooks that are written for mathematicians and publishers!! MY EXPLANATIONS WERE WRITTEN FOR STUDENTS WHO HAVE A HARD TIME UNDERSTANDING MATH!! And they are all FREE!!
There is also a video that might be helpful to you. To see all of my videos FREE (videos of me teaching in my younger years before I retired!!), look for "Rapalje Videos in Living Color." Choose "Intermediate Algebra" and look for the topic "Radicals and Fractional Exponents." If you happened to be interested in a video on Square Roots, I have a pretty good one there in Basic Algebra! Try the videos on a variety of topics from Basic, Intermediate, and College Algebra. As I said, everything is FREE. I'm not only not SELLING anything! I'm not even ADVERTISING for anyone!!
I hope you like my website!!! If you do, please recommend it to your family and friends!! At least check out the JOKE PAGE--all safe jokes for the little ears in your family!!
Merry Christmas!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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