Pre Algebra (Period 1)

More STAR Review

Person-Hours

 This little concept is almost always on the STAR
The number of hours it takes to complete a job

This job can be done by 1 person or multiple people.

So if a job requires 24 person-hours and you have 3 people working, each would need to work 8 hours a piece.
If you have 8 people working, each would only need to work 3 hours a piece.



Square Roots & Irrational Numbers: 11-1
Square root undoes squaring!

So you're looking for the the number/variable that was squared to get the radicand


1) RADICAL sign: The root sign, which looks like a check mark.

If there is no little number on the radical, you assume it's the square root

But many times there will be a number there and then you are finding the root that the number says.

For example, if there is a 3 in the "check mark," you are finding the cubed root.

One more example:
The square root of 64 is 8.
The cubed root of 64 is 3.
The 6th root of 64 is 2.


2)RADICAND : Whatever is under the RADICAL sign

In the example above, 64 was the radicand in every case.


3) ROOT (the answer): the number/variable that was squared (cubed, raised to a power)
to get the RADICAND (whatever is under the radical sign)


4) SQUARE ROOTS: The number that is squared to get to the radicand.
Every POSITIVE number has 2 square roots - one positive and one negative.

Example: The square root of 25 means what number squared = 25

Answer: Either positive 5 squared OR negative 5 squared



You can estimate non-perfect square roots by guess and check

Find the 2 numbers that it is between

Example: Square root of 52

It's between the 2 perfect squares: 49 and 64

So the square root is between 7 and 8

Since 52 is only 3 away from 49 and 12 away from 64, the square root will be closer to 7

Guess: 7.2 Square this: (7.2)(7.2) = 51.84 (adjust your estimate as necessary)

Real Number System 9-2
2 PARTS: RATIONAL AND IRRATIONAL (both real)



Review LEAP FROG number systems

I, RATIONAL NUMBERS (definitions of different number systems):

Natural = counting = 1, 2, 3, . . .

Whole = natural + 0 = 0, 1, 2, 3, . . .

Integers = whole + opposites = -3, -2, -1, 0, 1, 2, 3, . . .

Rational = integers and all the fractions/decimals in between - terminating and repeating decimals



II. IRRATIONAL - numbers like pi and square root of 3 - never repeat or terminate - round!