Monday, November 06, 2006
posted by JamieC at 4:30 p.m.

In today's class, we somehow fit two lessons in one day simply because I had to remind her that we didn't have math class tomorrow. Urgh... **groan** The mistake is mine, but the bad is not mine. the first part of class, we learned about multiplying and dividing radicals. When multiplying radicals, here is one rule, or example to follow.

Ex. - √a × √b = √ab which also happens to equal (ab)1/2.

That's easy enough to do though isn't it? Well of course, that example was just a review of what we've been doing in the previous days. It gets a little more complicated than that. Today, we also learned how to multiply radical binomials. Now this is pretty similar to the things we did in the first unit we did this year on polynomials and factoring them. In the following I will explain, [or try to...] the concept in a step-by-step process in the following example:

Simplify: 6√2 (√6 – 2√4)

1.) In order to simplify this, we must distribute the both the radical and the....oh...the other number, I don't quite know what the exact term is, but in this case it's the 6 right before the square root of 2. You multiply that with the same type of number of both sides of the binomial and then multiplying the radicals with the radicals resulting in...

6√2 (√6 – 2√4)
= 6√18 – 12√12

2.) After getting that answer, simplify the expression even more throughly, breaking it up bit-by-bit into more parts so that we are able to multiply it later on. [SiMpLiFy UnTiL yOu CaN nO lOnGeR sImPlIfY!!!]

6√2 (√6 – 2√4)
= 6√18 – 12√12
= 6√9√2 – 12√4√3
= 6 × 3 √2 -12 × 2 √3 = 18√2 – 24√3
Secondly, we were taught about radicals w/irrational denominators and what they had to do with dividing radicals-- which was pretty much everything...kind of. It was after all, in the form of a fraction, and a fraction is another expression of division. And this is what this might look like:

[click on box, because it's all screwed up.]

...where you divide the like terms [radicals with radicals] and then further simplify.

But when you are stuck in the situation where you have a radical binomial in the denominator, then it goes something like...

It is okay to have a radical in the numerator, but only then are numbers in their simplest form is when they do not have both a negative exponent and a radical in the denominator.

However, if there is a binomial in the denominator, the "difference of squares" must be multiplied. [REVIEW of DIFFERENCE OF SQUARES: Ex. (2x-3)(2x+3) = 4x2 - 9]

An example of this might be...

[click on the box again. I don't know why the other diagram is goofing up.]

...where the terms with difference of squares cancel each other out because of the positive and the negative.
And yes...finally, it's the end for me. At least I think it is...but if you wish to tweak your "rationalizing" skills, I found a website that can give you some online practice where you could answer some questions by filling in the blanks and then check your answer.
I apologize if you didn't get some of the stuff, even though the post was incredibly lengthy. I tried though. And just a quick reminder just in case you missed it. The homework for the rest of the week is Exercise 37 [omit 10/11/16/17/18] and Exercise 38 [omit 11/14/16/18].
The next person to blog is Kim Tran.


At November 06, 2006 10:23 p.m., Blogger Ms. Armstrong

Nice summary Jamie. I like how you reworded the entire lesson into your own wording instead of simply typing out the notes.
Could you please double check the rationalization of the denominator in the example with a binomial in the denominator. The work is not quite right. You need to change the sign to a negative to make it a difference of squares and put brackets around the original question so that you are distributing over the entire question. You also missed a term when you were typing in the ditributive property (the middle terms should cancel).
FABULOUS link. This will really help people to study for the quiz.