1. Square Roots, Rational & Irrational Numbers, Volume

2. Warm-up
Simplify.
1.) 8²
2.) 12²
3.) 2²
4.) 7²
5.) 4²
6.) 5²

3. Warm-up
Simplify.
1.) 3²
2.) 1²
3.) 10²
4.) 6²
5.) 9²
6.) 11²

4. Square Roots & Irrational Numbers
A number that is the square of an integers a perfect square
The inverse of squaring a number is finding a square root
An irrational number is a number that cannot be written as a ratio of two integers
A rational number is any number that can be written in the form of a/b(they can be written as fractions)

5. Characteristics of rational Numbers
Negative numbers can be rational numbers
Fractions are rational numbers
Repeating and terminating decimals are rational numbers
The square root of a number can be rational as long as it is a perfect square

6. Examples: Simplify each square root. 1.) √4 2.) √9 3.) √121
4.) √30
5.) √45
6.) √99

7. Examples: Identify each number as rational or irrational. 1.) √14
2.) √100
3.) …..
4.) ….

8. Homework
Textbook pgs #1-34

9. Square Roots Quiz Find the square root for each of the following.
1.) √ ) √196
2.) √ ) √64
3.) √ ) √121
4.) √ ) √16
5.) √ ) √144

10. Warm-up
Find the area the circles below with the given radii and diameters.
1.) r = 4 cm
2.) d = 10 m
3.) d = 8

11. Three dimensional figures
A three-dimensional figure, or solid, is a figure that does not lie in a plane
A flat surface shaped like a polygon is called a face
Each segment formed by the intersection of two faces is an edge
A prism is a three-dimensional figure with two parallel and congruent polygonal faces, called bases
The height of a prism is the length of a perpendicular segment that joins the bases

12. Types of 3-d figures
A cube is a rectangular prism with faces that are squares
A cylinder has two congruent parallel bases that are circles
A cone has one circular base and one vertex
A pyramid is a three-dimensional figure with triangular faces that meet at one point, a vertex, and a base that is a polygon
A sphere is the set of all points in space that are the same distance from a center point

13. Homework
Textbook pg. 439 #1-12

14. Volumes of rectangular prisms & cylinders
The volume of a three-dimensional figure is the number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges one unit long

15. Volume formulas Volume of a Rectangular Prism
V = area of base ∙ height
= length ∙ width ∙ height
***Area = base ∙ height or length ∙ width
Volume of a Cylinder
***Area(of circle) = πr²

16. Example(s): Find the volume of each of the following. 1.) 2.) 20 cm
1.) )
20 cm
14 cm
8 cm
17 cm
8cm

17. Example(s): Find the volume of each of the following. 3.) 4.) 2 in 8 m
3.) )
2 in
8 m
2 in
6 in
7 m

18. Homework
Textbook pgs #1-16 Evens Only

19. Warm-uP Find the area of each of the following. 1.) circle r = 4 mm
2.) square one side = 12 in
3.) triangle b = 10 ft, h = 8 ft