7.1 nth Roots and Rational Expressions In this section, we will… Use rational exponent notation Find nth roots Evaluate and simplify radical expression.

7.1 nth Roots and Rational Expressions

In this section, we will…

Use rational exponent notation

Find nth roots

Evaluate and simplify radical expression

7.1 nth Roots and Rational Exponents

RADICALS ARE SO RAD DUDE!!!!

7.1 nth Roots and Rational Expressions: nth Roots

If a is a non-negative real number, any number b, such that is the square root of a and is denoted

Examples: Evaluate the following by taking the square root.

2b ab a

121

16

2b a

Negative numbers do not have real # square roots

Recall from Review …

Vocabulary Vocabulary Important Properties Important Properties

RAD-TASTIC MATHEMATICS3

RAD-RRIFIC EXAMPLES

4Rewrite the expression using rational exponent notation.

Examples with

SWAGGER!

5Rewrite the expression using radical notation.

I’m too smart for my

calculator!!!

6Evaluate the expression WITHOUT a calculator.

Friday 10/7/11 HomeworkPg. 404 #13-22, #29-40

(even)

THANK YOU FOR

THE EXTRA

PRACTICE MS.

POBUDA!!

7

RADICAL REFRESHMENT

Section 7.18

WHITEBOARDIN G9

Real World Uses of Square Roots 10

http://www.youtube.com/watch?v=_TrFzF0ZE00

PROPERTIES OF RATIONAL EXPONENTS

Section 7.211

7.1 nth Roots and Rational Expressions: Simplify Expressions with Rational Exponents

Simplifying Expressions Containing Rational Exponents:

Laws of Exponents: For any integers m, n (assuming no divisions by 0)m n m nx x x

nm mnx x

n n nxy x yn n

n

x x

y y

0 1x

mm n

n

xx

x

1n na a m

nm

n m na a a new!

new!

1nn

xx

n n

x y

y x

1 nn

xx and

Recognize these?!?!

13

m n m nx x x

n n nxy x y

mm n

n

xx

x

n n

n

x x

y y

nm mnx x

1nn

xx

n nx y

y x

Properties of Exponents Applied to Radicals:

Simplifying Radicals: A radical is in simplest form when:

No radicals appear in the denominator of a fraction The radicand cannot have any factors that are perfect roots

(given the index)

Examples: Simplify each expression.

n n nab a bn

nn

a a

b b m

n m na a

12

50

3 16

7.1 nth Roots and Rational Expressions: nth Roots

Simplifying Radical Expressions Containing Variables:

Examples: Simplify each expression. Assume that all variables are positive.

5 5x

84 16x

7b

6 53 54x y

When we divide the exponent by the index, the remainder remains

under the radical

7.1 nth Roots and Rational Expressions: nth Roots

7.1 nth Roots and Rational Expressions: Add, Subtract, Multiply and Divide Radicals

Multiplying and Dividing Radical Expressions:

Examples: Simplify each expression. Assume that all variables are positive.

35 20x x

23

4 23

3

81

xy

x y

43 3 10

we will use: n n nab a b

we will use: n

naan

b b

we will use: m

n m na a

7.1 nth Roots and Rational Expressions: Rationalize Denominators

Rationalizing Denominators: Recall that simplifying a radical expression means that no radicals appear in the denominator of a fraction.

Examples: Simplify each expression. Assume that all variables are positive.

24

5

5

4 2

3

4

2

Adding and Subtracting Radical Expressions: simplify each radical expression combine all like-radicals

(combine the coefficients and keep the common radical)

Examples: Simplify each expression. Assume that all variables are positive.

125 20

2 12 3 27

2 2 3 338 25 8xy x y x y

544 32 2x x

7.1 nth Roots and Rational Expressions: nth Roots

7.1 nth Roots and Rational Expressions: Simplify Expressions with Rational Exponents

Examples: Simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive.

2 1 13 2 4x x x

344 8x y

1124

34

2 2

2

xy x y

x y

7.1 nth Roots and Rational Expressions: Add, Subtract, Multiply and Divide Radicals

Examples: Simplify each expression. Assume that all variables are positive.

5 8 3 3

2 2x x

2

2 3 5

4 2 3 5 2 8

Radical Maze 21

7.1 nth Roots and Rational Expressions: Applications

Example: The final velocity, v, of an object in feet per second (ft/sec)

after it slides down a frictionless inclined plane of height h feet is:

where is the initial velocity

in ft/sec of the object.

What is the final velocity, v, of an object that slides down a frictionless inclined plane of height 2 feet with an initial velocity of 4 ft/sec?

2064v h v 0v

Homework:

Tuesday: Finish Puzzle worksheet

Wednesday: Pg. 411-412 # 19, 20, 37-67 (odds)

7.1 nth Roots and Rational Expressions

7.1 nth Roots and Rational Expressions

From Math for Artists… “These are the laws of exponents and radicals in bright, cheerful, easy to memorize colors.”