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 4√45, and one of the sides measures 3√5, 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)
3√5 and 3√5 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.
Tonight's homework is Exercise 38, except for question 16. The Pre-test has been moved to tomorrow.
The next scribe is Arvee.
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