Transcript Warm-Up

Warm Up 09-08-09
Make a factor tree showing the prime
factors for the following numbers:
48
63
80
92
128
Radical Expressions
Simplifying Square Roots
Square roots

radical
Square roots are one type of _______
expression
__________.
 When asking for the “square root” of 36 you
are asking for a number that, when ________
multiplied
itself equals ____.
36
by ______
radical
sign
36 = 6
radicand
To Simplify Radical Expressions
All of the following must be true…
We just
work with
this today

The radical has no perfect square factors
other than 1. (Twins make a perfect square)

The radicand has no fractions.

There are no square roots in any
denominator.
Simplify the Square Roots
49
=7
What about 50 ?
 50 is not a _______
perfect _______.
square


so we will simplify… 2 methods
You choose which you prefer.
Simplify Square Roots – Method 1

Factor out the perfect square roots
50  25  2
 25  2
5 2
Check with a calculator to see that these match
Simplify Square Roots – Method 2
-Helpful when you don’t know perfect squares!

Factor the number in the radicand down to
prime numbers and simplify. (Look for
twins…they make perfect squares)
2 50
5 25
5

5

5

2
50
 5 2
Simplify

54
Method 1…
54  9  6  9  6
3 6

Method 2…
2 54
3 27
3
54 
3 3 3 2
9
3
 3 6
Simplify

48
Method 1…
48  16  3  16  3
4 3

Method 2…
48 
2 48
2 24
2 12
2 6
3
22223
 22 3
 4 3
What about…
33  3 11
33
No Perfect Square Factors
No twins!
Leave it as it is
33  33
Your turn! Simplify Using Either
Method
80 
75 
27 
56 
HOMEWORK
Write these out on your own paper
before you leave class.
Simplify the radicals…..Show your work!!!
32 
200 
108 
144 
90 
15 