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Homework #17
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WARM UPSimplify the expressions: 1.
2.
3.
4.
( 81 𝑥5 𝑦− 44 𝑥 𝑦−2 )12
Homework #16
Homework #17(4 𝑥3 𝑦5 ) (125 𝑥2 𝑦3 )
13
Radicals September 2nd
SIMPLIFYING RADICAL EXPRESSIONS
A radicand, the expression under
the radical sign, is in simplest form if it contains no perfect square factors other than 1.
Using prime factorization, we can simplify radical expressions
Radical or Square Root
PARTS OF A RADICAL Radical: Includes the symbol, radicand, and
index Radicand: Expression under the radical
symbol Index: The degree of the radicalThe index of this radical is 3. What does that mean?
RE-WRITE THE FOLLOWING1. x2 = ______
2. 8 = ______
3. 49 = ______
4. b5 = ______
So, what is … ?1. = ________
2. = ________
3. = _______
4. = _______
SIMPLIFY THE FOLLOWING
SIMPLIFY What happens if the radicand is not a
perfect square?Use prime factorization!
√24
FACTOR THE RADICANDbaab
* Try to find a perfect square
factor!
FACTOR THE RADICANDExamples:1. 3.
2. 4.
TRY THESE ON YOUR OWN1. 2.
WHAT HAPPENS WITH EXPONENTS?
TRY THESE1. 2.
HOMEWORK Radical Worksheet #1
WARM UPSimplify the Radical Expressions:
RATIONAL EXPONENTS The word “rational” means a
ratio of two integers, or fraction. Remember our fractional
exponents, these are referred to as rational exponents!
For example x1/2 OR 52/3
So why are we talking about exponents in the radical lesson?!
FILL IN THE CHARTS
x y49
16253649
y = √ xx y49
16253649
y = x(1/2)
TRY THESE CHARTS
x y18
2764
x y18
2764
3 xy 3/1xy
RE-WRITE AS RADICALS
1.
2.
3.
4/1x
7/1x
100/1x
RATIONAL EXPONENT TO RADICALGeneral Formula:
bcb c aa /So,
bca /
RE-WRITE AS RATIONAL EXPONENTS
1.
2.
3.
5 4x
1610
6 3b
**A radical can be written as a
rational exponent and a
rational exponent can
be written as a radical.
NOW, GO BACKWARDSWrite each expression as a radical
1.
2.
3. 5/3x
5/7x
3/18
LETS SOLVE ONEHow do we solve this?
Lets first re-write as a radical …
Now, is that easier?
2/34
JOBS THAT USE RADICALS Computer and Information Systems Managers Engineering ** Farmers/ranchers Agricultural Managers Funeral Directors Industrial Production Managers Medical and Health Service (**Athletic Trainers) Property, real estate, and community association managers Purchasing Managers Insurance Underwriters Forest Conservation and Logging Workers Aerospace Engineers Chemists Physicists and Astronomers Economists Teachers Registered Nurses Computer Control Programmers and Operators Architects and Interior Designers Financial Industry Electrical Engineering
Athletic Training:s = (√g * L)/12s = walking speed (ft/s)g = acceleration due to gravity (386 in/s)L = leg length (in)
WHAT HAPPENS IF THE RATIONAL EXPONENT IS NEGATIVE???
1.
2. 3.
2/1x
3/2x 2/34
THIS ALSO WORKS WITH VARIABLESExample 1 (perfect square):
Example 2 (with leftovers):Since this is a 3rd root you find three in your “pairs” not
just two!
33362/6 xxxxx
xxxxxxxx 23 2223 73/7
TRY THIS ON YOUR OWN
4 6532 yx
LETS SIMPLIFY1.
2.
7 57/2 xx
3
3 2
xx
CAN YOU FIND A PATTERN WHEN ADDING RADICALS?
HOW ABOUT WHEN WE SUBTRACT?
ADDING/SUBTRACTING RADICALSIn order to add/subtract radicals,
the _____________ must be the same.
To add/subtract radicals, simply add/subtract the________________.
PRACTICE: SIMPLIFYING RADICALS
1.
2.
NOW, TRY THESE
HOW COULD WE USE THIS?Find the perimeter of the
rectangle below.
CAN YOU FIND THE PATTERN WHEN MULTIPLYING RADICALS?
MULTIPLYING MONOMIAL RADICALSTo multiply monomial radicals
multiply their “outsides” together then multiply their “insides” together. Make sure you SIMPLIFY the radical completely!
PRACTICE: MULTIPLYING MONOMIAL RADICALS
1.
2.
3.
GEOMETRY APPLICATIONFind the area of the triangle
below.
DIVIDING RADICALS
Examples:
PRACTICE: DIVIDING RADICALS
9225y
RATIONALIZING We can never leave a radical in the
denominator of a fraction.
In order to get rid of a radical in the denominator, we have to “rationalize” the denominator.
In other words, we need to get the “rat” (radical) out of the “den” (denominator).
HOW DO WE GET RID OF A RADICAL???
So what operation gets rid of a radical?
RATIONALIZING THE DENOMINATOR
Are we allowed to just randomly multiply the denominator by something?
PRACTICE: RATIONALIZING
PRACTICE: RATIONALIZING
MORE EXAMPLES:
EXAMPLES:
HOMEWORK Radical Worksheet #2