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