chapter 7.3 Simplifying Radical Expressions.notebook
March 31, 2016
Bellwork:
Solve Factoring
Chapter 7.3(a) Simplifying Radical Expressions
2
2
1) 4y + 12y = ­9
2) 8x = 50
Use the product rule and the quotient rule for radicals. Be able to use the product and quotient rule to simplify radicals.
3) Write the equation of the line that is parallel to the line y = 8 and passes through the points (2, ­3)
Simplify:
4)
5) Mar 27­7:53 AM
Mar 27­9:37 AM
1) Multiplying with radicals
Look at the following pattern.
a.
b. c.
multiply inside with inside and outside with outside
Product rule for Radicals
If and d. e. are real numbers, then
Mar 27­9:38 AM
Mar 27­9:48 AM
Look at the following pattern.
2) Dividing with Radicals
a.
b.
c. d. Quotient Rule for Radicals
If and zero , then
are real numbers and Mar 27­9:54 AM
is not Mar 27­9:55 AM
1
chapter 7.3 Simplifying Radical Expressions.notebook
A radical expression is in simplest form when the following three statements are true:
March 31, 2016
We can use both the product and the quotient rules to simplify radicals.
3) Simplify the following radicals
> The expression under the radical sign has no perfect square (cube, 4th, etc) factors, other than 1.
> The expression under the radical sign does not contain a fraction
> The denominator does not contain a radical expression
a. b.
c.
Mar 27­10:03 AM
Mar 27­10:04 AM
Do you agree or disagree with the following statements. If you disagree rewrite it so that you do agree.
4) Simplify the following radicals
a. b.
> Agree/Disagree: The numbers under the radical get multiplied together.
> Agree/Disagree: The numbers that are in front of the radical get added together.
c.
Mar 31­9:51 AM
Mar 27­10:00 AM
The distance formula is one place where we use and simplify radicals. Using the Pythagorean Theorem: d
(x1, y1)
d2 = a2 + b2
(x2, y2)
b = y2 ­ y1
a = x2 ­ x1
4) Use the distance formula and find the distance between the following points. Simplify the radical if possible.
a. (­1, 3) and (­2, 6)
d2 = (x2 ­ x1)2 + (y2 ­ y1)2
b. (­3, 7) and (2, 3)
Distance Formula:
The distance between two points (x1, y1) and (x2, y2) is given by Mar 24­7:59 AM
Mar 24­7:59 AM
2
chapter 7.3 Simplifying Radical Expressions.notebook
March 31, 2016
We have simplified non­perfect square roots; now lets look at non­perfect cubes, 4th roots,... and simplify them.
Work with the person next to you on the simplifying radicals worksheet for the next 10 min.
Mar 24­8:00 AM
Mar 24­8:02 AM
5) Simplify the following radicals.
6) Simplify the following radicals.
a.
b.
a.
Look for perfect cubes, or factors that occur 3 times.
c.
d. b.
c. Mar 27­10:07 AM
Mar 24­7:54 AM
The midpoint of a segment is the point located exactly halfway between the two endpoints of the line segment. Midpoint Formula:
The midpoint of the line segment whose endpoints are (x1, y1) and (x2, y2) is the point with coordinates
M
P
3) Find the midpoint of the following line segments a. P(­2, 5) and Q(4, ­6)
R
b. P(­4, 3) and Q(2, 4)
Mar 27­10:09 AM
Mar 24­7:47 AM
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chapter 7.3 Simplifying Radical Expressions.notebook
March 31, 2016
Homework
Simplifying Radicals WS
Mar 24­8:18 AM
Mar 24­8:18 AM
4