Today was a review day complete with a pre-test, which, I think, provided a sneak preview for tomorrow's test. After the pre-test, we solved three problems involving radicals with our group, one of it was we were asked to find out which value was bigger: 4/cube.rt (2) or 2 cube rt.(4)Solving the equation, we find out that:
So, all in all, both of them are just the same numbers, just written differently. Mr. K says that teachers love to teach this lesson because there are so many ways to write a number, while students hate it, because there are so many ways to write a number. =)
Since we're having a test tomorrow, I decided to put a bit of review here.
The number set composes of natural numbers, whole numbers, integers, rational numbers (A.K.A fractions), irrational numbers, and imaginary numbers. Imaginary numbers we don't have to learn until next semester, in which I think almost everyone of us are taking Pre-Cal 30S. Natural numbers are counting numbers e.g (1,2,3,...)and uses the symbol N with a slash before it. Whole numbers are (0,1,2,3,...) and uses the symbol W with a slash before it too. Integers are negative and positive numbers (...,-2,-1,0,1,2,...) and use the symbol I. Rational numbers are basically numbers that can be written as fraction a/b where b≠0, and a and b are integers. Symbol is I. Lastly, irrational numbers are numbers that are non-terminating, non-repeating numbers e.g √2, √3, pi.
Product law: xa.xb=xa+b
Quotient law: xa/xb=xa-b
Power law: (xa)b=xab
Inverse law: x-a= 1/xa
Properties of Radicals
√ab = √a.√b
√a/b = √a/√b
As Mr. K would say, it is often easier to work with powers than radicals to simplify expressions like the ones below.
Radicals and Mixed Radicals
Entire radicals: √12, √75
Mixed radicals: 2√3, 5√3 *Mixed radicals are all simplified mixed radicals of the radicals above.
Adding, Subtracting, Multiplying and Dividing Radicals
*ALWAYS simplify radicals before adding, subtracting, multiplying and dividing them.
Adding: 2√3 + 4√3 = 6√3
unlike terms: 2√3 + 4√3 + 3√2 = 6√3 + 3√2 = 3(2√3 + √2) note: Leave the unlike radical alone, applies to both adding and subtracting.
Subtracting: 2√3 - 4√3 = -2√3
unlike terms: 2√3 - 4√3 -3√2 = -2√3 - 3√2
Multiplying: √x(√a+√b) = √xa + √xb
Dividing: 1) √x/√a = √x/√a . √a/√a = √xa/a
2) √x/b+√a = √x/b+√a . b-√a / b-√a = xb-x√a/b2-a
I think that pretty much sums up the unit, I'm sorry for the length of the post. Next day's scribe is kimc, and don't forget that the Trigonometry Assignment is due tomorrow, and we have a test.