Transcript Do Now 6/7/07

Chapter 11
Final Exam Review
Section 11.2 “Simplify Radical Expressions”

A radical expression is in simplest form if the
following conditions are true:
-No perfect square factors other than
1 are in the radicand.
-No fractions are in the radicand.
-No radicals appear in the
denominator of a fraction.
Product Property of Radicals

The square root of a product equals the product of the square
roots of the factors.
4x  4  x 2  x  2 x
Quotient Property of Radicals

The square root of a quotient equals the quotient of the square
roots of the numerator and denominator.
a

b
a
b
21

81
21
21

9
81
Rationalizing the Denominator

Whenever there is a radical (that is not a perfect
square) in the denominator, the radical must be
eliminated by rationalizing the denominator.
5
7
5 7
5 7



7
49
7
7
Need to
rationalize the
denominator
Multiply by 1
Product property
of radicals
Simplify
Adding and Subtract Radicals

You can add and subtract radicals that have the
same radicands.
4 10  2 13  9 10
 2 13  5 10
Think of as combining ‘like terms’
5 3  48  5 3  16 3
5 34 3
Look for common radicands
9 3
Simplify
Multiplying Radical Expressions

You can multiply radical expressions the same way you multiplied
monomials and binomials using the distributive property and
FOIL.
5(4  20) ( 7  2 )( 7  3 2)
4 5  100
4 5  10
49  3 14  14  3 4
simplify & combine like terms
7  2 14  6
1  2 14
Section 11.3 “Solve Radical Equations”

An equation that contains a radical expression
with a variable in the radicand is called a radical
equation.
2
2
a

b
,
If
then a  b
If x  3, then ( x )  3
2

2
To solve a radical equation, you need to
ISOLATE the radical on one side and then
square both sides of the equation.
Section 11.4
The Pythagorean Theorem

For any RIGHT TRIANGLE, the sum of the
squares of the lengths of the legs, a and b, equals the
square of the length of the hypotenuse, c.
c
a
b
a b  c
2
2
2
The Right Triangle
a b  c
2
2
2
hypotenuse
(always across from the right angle
and always the longest side ).
c
a
legs
b
right angle
(90°)
Section 11.5 “The Distance and
Midpoint Formulas”
Distance Formula
y
To find the distance
between two points
( x2 , y2 )
( x1 , y1 )and( x2 , y2 )
( x1 , y1 )
x
d  ( x2  x1 )  ( y2  y1 )
2
2
Section 11.5 “The Distance and
Midpoint Formulas”
y
Midpoint Formula
The midpoint (middle point) between
two points can be found by:
 x1  x2 y1  y2 
,


2 
 2
( x2 , y2 )
( x1 , y1 )
x