Square Roots, Rational & Irrational Numbers, Volume

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

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

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)

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

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

Examples: Identify each number as rational or irrational. 1.) √14 2.) √100 3.) 0.323223222….. 4.) 0.232323….

Homework Textbook pgs. 428-429 #1-34

Square Roots Quiz Find the square root for each of the following. 1.) √36 6.) √196 2.) √49 7.) √64 3.) √81 8.) √121 4.) √225 9.) √16 5.) √169 10.) √144

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

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

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

Homework Textbook pg. 439 #1-12

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

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

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

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

Homework Textbook pgs. 451-452 #1-16 Evens Only

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