Simplifying Radicals (with work).notebook
December 21, 2015
Simplifying
Simplifying Radicals
Radicals
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2
1
54
How Do We Get
From Here
To There
54
3 6
1
Simplifying Radicals (with work).notebook
December 21, 2015
I KNOW, I KNOW,
pick me, pick me!!!
List all of the perfect squares between 1 ­ 400
1,4,9,16,25,36,49,64,81,100, 121,144,169,196,225,289,324,361,400
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Simplifying Radicals (with work).notebook
December 21, 2015
1,4,9,16,25,36,49,64,81,100, 121,144,169,196,225,289,324,361,400
Simplify:
1,4,9,16,25,36,49,64,81,100, 121,144,169,196,225,289,324,361,400
Simplify:
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Simplifying Radicals (with work).notebook
December 21, 2015
1,4,9,16,25,36,49,64,81,100, 121,144,169,196,225,289,324,361,400
What happens if you don't choose the largest perfect square?
Simplifying
Simplifying Radicals
Radicals
54
Before we start simplifying
radicals, we need to discuss
numbers in "exact form".
In general all integers, fractions, radicals and
the numbers e and π are considered to be exact
numbers and all numbers written in floating point
form (i.e. with a decimal point) are considered to
be approximate numbers.
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Simplifying Radicals (with work).notebook
December 21, 2015
Simplifying
Simplifying Radicals
Radicals
This is an example of an
"exact form" fraction.
This is an example of an
"approximate" fraction.
.33
but it is really .3333333333333333333333333333333
33333333333333333333333333333...
Simplifying
Simplifying Radicals
Radicals
This is an example of an
"exact form" radical.
This is an example of an
"approximate" radical.
7.35
but REALLY 7.3484692283495345 keeps
going and going and going and going
and going....
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Simplifying Radicals (with work).notebook
December 21, 2015
Simplifying
Simplifying Radicals
Radicals
108
Here Is
Another Method
List all the perfect squares from 2 - 12.
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
Simplifying
Simplifying Radicals
Radicals
108
Here Is
Another Method
Find the largest perfect square that will
divide evenly into the radical.
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
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Simplifying Radicals (with work).notebook
December 21, 2015
Simplifying
Simplifying Radicals
Radicals
108
Here Is
Another Method
Factor the two numbers to make the radical.
3 36
Simplifying
Simplifying Radicals
Radicals
108
Here Is
Another Method
Rewrite and pull out the perfect squares.
62 = 36
6
3 36
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Simplifying Radicals (with work).notebook
December 21, 2015
Simplifying Radicals
Evaluate each expression.
1,4,9,16,25,36,49,64,81,100, 121,144,169,196,225,289,324,361,400
(a)
(b)
(c)
(d)
1,4,9,16,25,36,49,64,81,100, 121,144,169,196,225,289,324,361,400
Practice Problems
162
­5 700
1152
9x 432
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Simplifying Radicals (with work).notebook
December 21, 2015
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Simplifying Radicals (with work).notebook
December 21, 2015
Simplifying Radicals
Product Property of Square Roots
The square root of a product equals the product of the square roots.
Quotient Property of Square Roots
The square root of a quotient equals the quotient of the square roots.
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Simplifying Radicals (with work).notebook
December 21, 2015
Evaluate each expression.
(e)
(f)
(g)
(h)
Simplify the following expression:
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Simplifying Radicals (with work).notebook
December 21, 2015
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Simplifying Radicals (with work).notebook
December 21, 2015
Adding & Subtracting Radicals
1)
2)
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Simplifying Radicals (with work).notebook
December 21, 2015
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Simplifying Radicals (with work).notebook
December 21, 2015
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Attachments
Mental Math Multiplication.ppt