Transcript Lesson 11.2 Simplifying Radicals

Warm up
Estimate the following radicals.
1.
80
2.
 8.9
4.
13
 3.6
5.
38
 6.1
3.
52
6.
 7.3
104
 10.2
125
 11.2
Lesson 11.2
Simplifying Radical Expressions
(Numbers Only)
SWBAT: Multiply and simplify radical expressions
containing numbers
Review:
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 or both.
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.
Let the escape begin…
Step 1: Figure out the number of “guards”
in the prison. The index is the
number of guards.
2
How many guards are there in the
following
problems?
7
3
2
12
7
64
8
3
18
Step 2:
Figure out how many prisoners (the
radicand) are going to escape. In order to do this
we must create a factor tree to determine how
many groups there are
The number of guards determine the number of
prisoners in each group trying to escape.
Simplifying Radicals with Numbers.
Simplify the following.
20
Step one, break the number down into a factor tree.
20
10
2
2
Step two: Circle any pairs.
The pairs bust out of the klink.
5
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 (the pair of 2’s) go charging at the
guards…but, only one gets away. One gets caught and is
never seen or heard from again. And the third guy (the
5), 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…
20
which is really just…
2 25
This guy gets away
This guy gets
caught and is
never heard from
again
so it ends up like this…
2 5
The guy that
got away
The guy left in
prison
This guy didn’t
have a partner
and so is left in
prison
But teacher,
teacher, what
happens to the
other guy?
He’s Dead, gone,
went bye bye,
won’t see him
again!
Another Example
Simplify the following:
140
Step 1: Make a factor tree
140
10
14
2
So that leaves: 2 7  5
Which is: 2 35
7
2
5
Your Turn!
Simplify the following:
1. 44
2 11
2.
64
8
3.
56
2 14
4.
250
5 10
Summary:
To simplify radicals I must …
Homework: Radical Worksheet