# - Algebra 1 ... Notes ...

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Algebra 1
Notes
Name: ________________________
Period: _______Date: ____________
Questions/Main Ideas:
TOPIC: Square roots and Cube roots
What is a square?
CLOs: Identify squares and cubes. Distinguish between a perfect squares and cubes
When we multiply an integer by itself we call the product the square of the number.
Why might this be?
What is a cube?
If 4 x 4 = 16, then we can say the square of 4 is 16 and it is written as ______.
What is an integer?
Draw a picture to illustrate why we call these products squares.
Draw a number line that
includes negative numbers.
Listening: You'll hear different words used when people talk about squares.
Square of a number :
A squared number:
3 squared:
you’ll hear
What's the square of 9?
Perfect square:
illustrate
Square Roots
written as
You can think of finding square roots as the inverse of finding squares. You find the
square root of a number (let's call it number A) by finding the number that, when
multiplied by itself produces number A. The examples below show this:
Think of these examples: 4 x 4 = 16 and - 4 x - 4 = 16.
Positive numbers have two square roots; a positive (called the principal square root)
and a negative. The symbol
find-finding
n means give the principal square root.
Try these:
25 
 16 
 100 
What happens if the negative is inside the radical?
inside
9 
let’s
do some thinking
Let’s do some thinking.
Suppose you were asked to find
lie between
40 ?
Is the answer an integer? ____________________
What two squares does 40 lie between? ______________________________
So, the square root of 40 is between which two numbers? _____________________
closest to
Which number do you think it would be closest to and why? ____________________
Use you calculator to find
Draw a square.
Plot this on a number line.
Draw a cube.
Try these: Find the root. Give you answers to the nearest tenth and graph on a
number line.
15 
What is DIMENSION?
How many dimensions does a
square have?
51 
 8
When we multiply an integer by itself then by itself again, we call the product the
cube of the number. Why might this be?
How many dimensions does a
cube have?
If 2 x 2 x 2 = 8, then we can say the cube of 2 is 8 and it is written as ______.
Draw a picture to illustrate why we call these products cubes.
Try these:
3
 3 125 
27 
3
8 
This time, we can have the negative under the radical. Can you simplify that one?
Can you estimate
line?
3
50
Identify the following parts of a radical:
n
a
Let’s learn how to simplify radicals. That is, put the radical in simplest form.
Examples:
1)
24
2)
12
3)
72
4)
3
72
Examples:
64 y 6
1)
2)
3
24x 6 y 4 z 7
You Try:
3
3)
Summary:
125x12
4)
243x15 y 8 z 9
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