P3. Radicals and Rational Exponents

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