Language of Mathematics II (48): Reducing Radicals

Table of contents listing all instructional math videos available from Chycho TV at http://www.chycho.com/?q=math_Table_Contents

List of videos that are available for download at http://www.chycho.com/?q=math_download_chycho

INTRODUCTION:
http://www.chycho.com/?q=Introduction_Instructions

During the last few years the education systems in Canada and the United States have been eroding. Students have been crammed into larger class sizes while the quality of teaching has deteriorated, in large part due to a lack of funding from local and federal governments.

John Ralston Saul, one of Canada's most celebrated authors and essayist, has warned us that "Canada's democracy... is eroding with every dime deducted from education budgets."

I have stated previously that I believe "as a collective we must understand that democracy can only exist in a society with an educated populace, and the right for self-governance can only be obtained through knowledge." I also believe that as long as the Internet remains Neutral, we, as a global community, can make a difference. We can fill the gap left behind by our governments and be proactive in educating our children

Sharing our communal experiences and knowledge is the essence of the Internet and chycho.com is proud to be a part of this movement. The information contained and conveyed through this medium is what will shape our future, and this site was created to represent a unique personal perspective and to contribute in bringing about positive changes.

As a result I have decide to produce instructional math videos to help those that want to improve their abilities in communicating in the language of mathematics. The videos are available on Chycho TV Located in the top right corner of http://www.chycho.com. Even though these videos are geared towards high school students, they will also help those in elementary school and those that are struggling with certain college and university courses.

The format of the videos is as follows: Lessons are in large part self contained and most have exercises which should be completed before proceeding to the next lesson. To help people understand a specific topic I have included answers to the exercises.

During the next few weeks and months, possibly years, I hope to be able to provide a vast library of resources for those that wish to finally understand the language of mathematics.

If there are certain areas that you are having problems with or wish me to discuss further then please send me a message or post a comment at my website. Even though I can not guarantee that I will be able to properly represent a topic I will try my best to produce a lesson if there is strong enough demand for a specific topic.

I hope these videos will help people learn how to communicate in the language that we have chosen to understand the world around us in a scientific manner, in the language of mathematics.

Best

Chycho
http://www.chycho.com/

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[chaospoet]

OK there's something I'm not quite getting: why is there still a cubed root in the final answer? If you've "paid the toll", as you put it, why is it still there? Why isn't the final answer 10a cubed, b, to the square root of 4a squared with the radical gone? I just keep expecting, for the sake of balance on both sides of the equal sign, for it to be gone. I don't understand why it's still there. I seem to be missing something in the logic of the equation here.

[chychochycho]

the cube root symbol is still there because everyone that was inside couldn't come out. The only way you can come out is to group yourself with three identical things. If you can't group into threes then you can't come out. And if there is anything that can't come out, then the cube root symbol stays. Those numbers and variables inside are stuck until they can group in threes.

hope that makes sense?

[chaospoet]

@chychochycho I think I got you. So this isn't like fractions for example where after you break things down into their prime factors you cross cancel like terms? I think that's what's confusing me. I keep thinking if you have a radical of 3 outside the root and you have say 5 of something (a to the power of 5) that three of those would cancel out the cubed radical outside the root symbol so you'd just end up with a root symbol with a 2 inside of it. That's what I keep expecting.

[chychochycho]

Yap, now you got it. It's NOT like division where you cancel terms. The 3 stays there, it's attached to the root symbol. The only time you don't write the cube root (the whole symbol) is when there is nothing left inside of it, so you don't need it anymore. Easy as pie :)

[MistaThrill]

im a straight A student ive never had to study things just came to me.... this didnt but u explained it in a way i can understand THX

[chychochycho]

glad to help :)

[liangqiaokajia]

love your vids! I forced all my friends in Geometry to watch ur videos and all of them said it was very helpful! thanks a lot!

[skatezombie808]

that's what im SAYIN! why can't they just talk NORMAL like this guy?? jeez.. math jargon is so ridiculous.

oh, thanks again chycho.

[chychochycho]

me too, and it's definitely my pleasure :)

[Timzsk8]

Thanks Chycho!!! I'm so glad I suscribed!

[chychochycho]

my pleasure, glad it helps :)