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Simplifying RadicalsDefinitely radical, debatably simple.
Simplifying Radicals
So What is a Radical…?
A Radical is nothing more than a square root sign
EXAMPLES:
The expression is read as “radical 20” and
The expression is read as “ 5 radical 3.20
5 3
Simplifying Radicals
There are some radicals easy to simplify…
For Example:
and
Other radicals take more work…
Like:
and … neither has an easy
answer, but both can be simplified
25 5 196 14
75 128
Simplifying Radicals
So how do we simplify and … ?
Let’s start with .
Check with a calculator: and
Now let’s try .
75 128
75
75 ( 25)( 3) 5 3
75 8.66 5 3 8.66
128
128 ( 64)( 2) 8 2
Simplifying Radicals
So what are the rules? What steps can I follow?
Step 1: Either know or have a list of your perfect squares present. 4,9,16,25,36,49,64,81,100…
These are the numbers that have nice sqrts.
Step 2: Determine if any of the square roots divide into your radical evenly. Let’s try :
50/4 =12.5
50/9 = 5.555
50/16 = 3.125
50/25 = 2
50
So 50 = 25 x 2
Simplifying Radicals
Step 3: Rewrite the radical as the product of two parts.
Step 4: Replace the radical that has a perfect square root with a regular number.
The answer is read “5 times the square root of 2”
or “5 radical 2”
50 25 2
50 25 2 5 2
Simplifying Radicals
The are other ways to simplify as well… Sometimes we can just use multiplication and division.
For Example:
and
There are also some radicals that cannot be simplified…
cannot be broken into two parts.
6 5 3048
124
31
Simplifying Radicals
There is one final method of simplification that we must consider.
We are allowed to multiply two radicals or divide two radicals, BUT you cannot divide a regular number by a radical.
Example:
So what to we do… ?
10
2
Simplifying Radicals
We have to “rationalize the denominator”…
Step 1: Multiply the top and bottom of the fraction by the bottom.
Step 2: Simplify
Step 1
10
2
2
2
10 2
4 10 2
2 5 2
These =
Simplifying Radicals
Let’s try two problems…
64 2
30 8
Simplifying Radicals
HW: P 355 (1-23 odd)
Work on this assignment in pairs for the remainder of class.
