Download Warm up 1-5-2010

Warm up 1-8-12 week 3-1
Break the following down in to factors. If
there are a common pair of factors at the
end, circle them. If the factor does not
have a match, put a square around it.
1. 80
4. 120
2. 76
5. 20
3. 64
6. 24
Simplifying Radical
SWBAT: Multiply and simplify radical
expressions containing both numbers and
variables.
Write down the first 20 perfect squares
like this 12 = 1
22 = 4
The parts of a radical
The index. The number
above the “tail.”
Normally it is a 2 and
isn’t even written.
The radical bar. Kind
of like a division sign
with a tail
7
x
4
The Radicand. The “stuff”
underneath the radical bar,
can be numbers or variables.
How to Simplify Radicals
The radical bar is kind of like “math” prison.
Anyone that can, wants to get out of
prison.
But there are guards, so in order to bust out
of the joint the numbers always break out
in groups.
The size of the group depends on the
number of guards.
Step 1: Figure out the number of “guards” in
the prison. The index is the number of
guards.
How many guards are there in the following
problems?
x
5
7
x
5
x
8
3
z
Step 2: Figure out how many prisoners (the radicand) are
going to escape.
The number of guards determine the groups trying to
escape.
For example:
x
3
has how many guards?
2
How many prisoners are there?
3
The Great Escape
So here is how it goes down. Those 3 prisoners, not very
smart, see that there are only two guards and think, hey,
two of us can charge the guards and get away.
So two of the prisoners go charging at the guards…but,
only one gets away. One gets caught and sent to
solitary confinement and is never seen of or heard from
again. And the third guy, since he didn’t have a partner
to charge the guards with, he’s left to rot in prison.
That’s what happens when you lead a life of crime.
So…
x
3
which is really just…
x x x
This guy gets away
This guy didn’t
have a partner
and so is left in
prison
This guy gets
caught and is
never heard from
again
so it ends up like this…
The guy that
got away
x x
The guy left in
prison
But teacher,
teacher, what
happens to the
other guy?
He’s Dead, gone,
went bye bye,
won’t see him
again!
Here’s another example.
How many guards?
2
How many prisoners?
5
How many are going to try
to bust out?
4
Why only 4?
The 5th guy doesn’t have a
partner.
x
5
How many actually make it
outside if 4 try to
escape?
2
How many are left in
prison?
1, he didn’t have a partner.
So then the simplified
form of x5 is…
xx x
or x
2
x
Another Example
Simplify the following radical expression.
x
6
How many guards?
How many prisoners are going to try to escape?
How many left inside to rot?
How many make it out of the big house?
3
What is the answer?
x
Try these by yourself. They all
follow the same steps.
x4
1.
2.
3.
3
x
7
x3 y 2
4. abc
Little different, how many “guards”
What about numbers?
What do you do if there are numbers
underneath the radical instead of
variables?
Exactly the same thing…except
You must break down the number into a
“factor tree.”
Simplifying Radicals with Numbers.
Simplify the following.
20
Step one, break the number down into a factor
tree.
20
10
2
2
5
Step two: Circle any pairs.
The pairs bust out of the klink just like normal.
20
10
2
2
5
Only one makes it out, if you didn’t have a partner
to escape with, then you rot.
So the answer is…
2 5
Another Example
Simplify the following:
140
140
Step 1: Make a factor tree
10
14
2
So that leaves:
Which is:
2 75
2 35
7
2
5
You Try
Simplify the following:
5. 44
6.
64
7.
38
8.
125
Try Some Difficult Ones.
Same rules (steps)!
8x3 y 2
9.
3
10.
27
11. 4 32x3 z8
12.
5
5
Put on your notes
– this is a
continuation of
yesterday’s stuff
Multiplying and Dividing Radicals
The rules to multiply and divide radicals are:




You can multiply and divide radicals with other
radicals
Multiply or divide the terms outside
Multiply or divide the terms inside the radical
Simplify completely
6 2
6
2
Multiply the radicals then
simplify


Example :
Example :
2 3x  4 6 x 2
8ab 2  10 10a3b 4
Last thing you need to know about
radicals.
Last thing: You may not leave a radical in a
denominator!
Catch that, no radicals in the bottom of a
fraction!
If there is a radical in the denominator, you
have two options.
The Two Options Are…
Option A: Check, maybe you can simplify
with the numerator.
Example:
18
 6 (is this simplified ?)
3
Option B: Called RATIONALIZING
Multiply the numerator and denominator by the
radical in the denominator.
Example:
3 5
15
15



5
5 5
25
Last Ones, I Swear
13.
8
3
14.
32
8
15.
1
3
16.
8
16
Summary: To simplify radicals I
must …

Classwork: simplify the following 8
problems (put it on the back of your notes)
1. 9 x 2
2.
4.  2 18a b
6
6. 2 50ab
5
x3
2
3.
75 x 2 y 3
4
5. 8 300 x y
7.
14 5 6
15a b c
Homework: Radical Worksheet
17
8.  5 162 x