Squares cubes and roots edmodo 2013 14
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Transcript of Squares cubes and roots edmodo 2013 14
Squares, Cubes and Roots
8th Grade Math 2013-14
MCC8EE2, MCC8NS1, MCC8NS2
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
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
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
Perfect Square Activity
What is a Root?
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
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
4
16
25
100
144
= 2
= 4
= 5
= 10
= 12
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
Perfect Squares
1
4
916
253649
64
81
100121
144169196
225
256
324
400625
289
361
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
Non-Perfect Squares
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
Perfect Cubes
Perfect Cubes
• How do you find the volume of a cube?
2cm
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
Perfect Cubes
• What is the volume of this cube?
• What is the root of this cube?
Perfect Cubes
• What is the volume of this cube?
• What is the root of this cube?
Perfect Cubes
• What is the volume of this cube?
• What is the root of this cube?
Let’s Practice
1. 4.
2. 5.
3. 6.
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
Perfect Cubes1 -1
8 -8
27 -27
64 -64
125 -125
216 -216
343 -343
512 -512
729 -729
1000 -1000
Compare Numbers• Compare the following numbers by placing
<, >, <, >, or = in the box.
1. 5
2. 8.5
3.