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**Square Roots, Rational & Irrational Numbers, Volume**

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

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

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**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)

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**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

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**Examples: Simplify each square root. 1.) √4 2.) √9 3.) √121**

4.) √30 5.) √45 6.) √99

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**Examples: Identify each number as rational or irrational. 1.) √14**

2.) √100 3.) ….. 4.) ….

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Homework Textbook pgs #1-34

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**Square Roots Quiz Find the square root for each of the following.**

1.) √ ) √196 2.) √ ) √64 3.) √ ) √121 4.) √ ) √16 5.) √ ) √144

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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

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**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

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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

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Homework Textbook pg. 439 #1-12

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**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

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**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

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

1.) ) 20 cm 14 cm 8 cm 17 cm 8cm

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**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

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Homework Textbook pgs #1-16 Evens Only

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**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

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