p3. radicals and rational exponents
DESCRIPTION
P3. Radicals and Rational Exponents. Ch. P3: Radicals and Rational Exponents. SIMPLIFY EVALUATE using order of operations (Ex #1). Definitions. Radical sign Radicand Radical Expression Principal Square root Simplify a square root Conjugates. RULES for Square Roots. - PowerPoint PPT PresentationTRANSCRIPT
P3.Radicals and Rational Exponents
Ch. P3: Radicals and Rational Exponents
SIMPLIFY EVALUATE using order of operations (Ex #1)
• Radical sign
• Radicand
• Radical Expression
• Principal Square root
• Simplify a square root
• Conjugates
Definitions
The Product Rule
• If a and b represent nonnegative real number, then
• If a and b represent nonnegative real numbers and b does not equal 0, then
RULES for Square Roots
The Quotient Rule
Adding and Subtracting
You may only add “like” radicals
Square Roots of Perfect Squares
The principal square root of a2 is the absolute value of a.
a2 a
In other words, the principal square root of a2 is the positive root!
Ex:
To simplify means ______________
Ex#2a. b.
Ex #3a. b.
Simplify with
Product & Quotient
rule:
YOU TRY:
Ex#4a. b.
Ex #5a. b.
Adding/ Subtracting
Like Radicals
YOU TRY:a. b.
a. b.
APPLY:Simplify
Evaluate the following:
Let’s go back to yester-year….
THE TRICK? RATIONALIZE THE DENOMINATOREvaluate the following:
Ex #6RationalizeThe
Denominator
Ex #7Rationalize
with Conjugates
The End (Day 1)
HW: pg. 42 #1-53 odd
Radicals and Rational Exponents (DAY 2)
OTHER POWERS
QUESTION OF THE DAY
• WHAT RULES DO YOU ALREADY KNOW ABOUT EXPONENETS? (WARM UP RELATED TO THIS)
• THEN Discovery activity (next slide)• HOW ARE RADICALS AND RATIONAL
EXPONENTS RELATED TO EACH OTHER?
Use your calculator to complete the table below:
1. What do you notice about your answers to the problems in the same row?
2. Is there some pattern that relates the two expressions in each row to one another? Describe the pattern.
3. Given the expression , what expression using a root symbol would yield the same numerical value?
4. Given the expression what expression utilizing a fractional exponent would yield the same numerical value?
Expression Numerical Value Expression Numerical Value
• Rational exponents
• Index
• Also, if
Definitions
Ex #8Simplify
Higher Roots
YOU TRY:
Ex #9
You try:
CombiningCube Roots
(Refer back to warm up)Ex #10•
Ex #11•
Using definition of
am/n
Ex #12• (5x1/2)(7x3/4)
Simplifying Expressions
withRational
Exponents