7.1 nth roots and rational expressions in this section, we will… use rational exponent notation...
TRANSCRIPT
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.”