## Wednesday, November 19, 2008

### Layers [scribe - 11/19/2008]

There is a difference between

and

The most obvious (and often overlooked) difference is the base. Also, the former will give a solution and the latter won't.

Our first example (the former) will give a solution:

Let's just ignore the negative for a few seconds. The number then becomes

This works out to be 10.

Now that a few seconds are over, the negative will be brought back in and will act as -1 multiplied by 10. So,

Our second example (the latter) doesn't end as well.

The point of finding a square root is to find a number, when is multiplied by itself will give us the base.

When one thinks about it, the are no numbers that can be multiplied by themselves to give us -100. This is the very reason why we can't find the root of a negative number.

=============================

The other thing covered in class today was solving area problems using radicals.

For instance,

If the area of a rectangle is 445, and one of the sides measures 35, what does the other side measure?

Solving this problem is simpler than it seems; all that actually needs to be done is to divide the two radicals given.

-find two factors of 45

-"Pull out" the perfect square. In this case the perfect square is 9 -->(3)(3)

35 and 35 cancel out. The answer is 4.

But what if the measurements of two sides were given instead of one side and the area?

What if the measurements were:

and

?

In this case we would have to multiply.

=

And in case you forgot, the square root of 4 is 2.

The problem is freakishly straightforward from this point on, and the answer is 7.

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Tonight's homework is Exercise 38, except for question 16. The Pre-test has been moved to tomorrow.

The next scribe is Arvee.