squares cubes and roots edmodo 2013 14
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Squares, Cubes and Roots
8th Grade Math 2013-14
MCC8EE2, MCC8NS1, MCC8NS2
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POD 17 Sep Evaluate1. –122
2. (a4b3)(a5b2)
Simplify; write solution in Scientific Notation:
3. 3 x 10-3 • 4 x 104
4. .00065 x 103
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POD 18 SepUse the information given to find the measures of:1. angle d
l1 || l2 and l3 || l4
l1
l2
l3 l4
ab
c
de
fg
h
j ki
540
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SquaresWhat is this shape?
How do you know?
What is the area?
How many small squares areinside the large square?
What is the perimeter?
8181
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Perfect Square Activity
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What is a Root?
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SquaresWhat is a root?
What is the area ofthis square?
What is the root?
Is there any other number Multiplied by itself that equals16?
4
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Perfect Squares
• 0 x 0 = 02 = 0• 1 x 1 = 12 = 1 -1 x -1 = (-1)2 = 1• 2 x 2 = 22 = 4 -2 x -2 = (-2)2 = 4• 3 x 3 = 32 = 9 -3 x -3 = (-3)2 = 9• 4 x 4 = 42 = 16 -4 x -4 = (-4)2 = 16• 5 x 5 = 52 = 25 -5 x -5 = (-5)2 = 25• 6 x 6 = 62 = 36 -6 x -6 = (-6)2 = 36• 7 x 7 = 72 = 49 -7 x -7 = (-7)2 = 49• 8 x 8 = 82 = 64 -8 x -8 = (-8)2 = 64• 9 x 9 = 92 = 81 -9 x -9 = (-9)2 = 81• 10 x 10 = 102 = 100 -10 x -10 = (-10)2 = 100
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4
16
25
100
144
= 2
= 4
= 5
= 10
= 12
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Notes• The root of a square (square root) is equal
to the length of one side of the square• All squares have two roots, one positive
and one negative• Perfect squares have integers for roots• A Radical is the symbol we use to identify
roots• A Radicand is the number or variable
inside the radical 25
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Perfect Squares
1
4
916
253649
64
81
100121
144169196
225
256
324
400625
289
361
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Estimating Non-Perfect Squares
0 5 101 2 3 4 12119876
• Squares that do not have an integer for a base are called non-perfect squares. For example is a non-perfect square because no integer multiplied by itself equals 20.
• We estimate non-perfect squares by finding which perfect squares they are between:
20
2016 25
16 25
4 55.4
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Non-Perfect Squares
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Let’s Practice
0 1 2 3 4 5 6 7 8 9 10
Plot:
1. 4.
2. 5.
3. 6.
6
30
55
15
90
75
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Perfect Cubes
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Perfect Cubes
• How do you find the volume of a cube?
2cm
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Perfect Cubes
• How do you find the root of a cube?• The length of 1 side of a square is the
square root, and the length of 1 side of a cube is the cube root
8cm3
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Perfect Cubes
• What is the volume of this cube?
• What is the root of this cube?
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Perfect Cubes
• What is the volume of this cube?
• What is the root of this cube?
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Perfect Cubes
• What is the volume of this cube?
• What is the root of this cube?
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Let’s Practice
1. 4.
2. 5.
3. 6.
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Notes• The root of a cube (cube root) is equal to the
length of one side of the cube
• Perfect cubes have integers for roots
• A small 3 in the hook of the Radical identifies the third, or cube root
• Cubes can have a negative Radicand
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Perfect Cubes1 -1
8 -8
27 -27
64 -64
125 -125
216 -216
343 -343
512 -512
729 -729
1000 -1000
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Compare Numbers• Compare the following numbers by placing
<, >, <, >, or = in the box.
1. 5
2. 8.5
3.