Download Day 5

Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Perfect Square ­ Any whole number that can be represented as the area of a square with a whole number as its 5
side length is a perfect square
5
25 is a perfect Square!!
Area = b x h
= 5 x 5
= 25
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
5
5
Square Root ­ A number for which, when multiplied by itself, results in a given number.
52 = 25, therefore 5 is the square root of 25
25 = 5
**The side length of the square is the square root of the area.
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Using Prime Factorization
1. Write the prime factorization of the number.
2. Group the prime factors into pairs.
3. Take one number from each group, then multiply 5
Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
What is the square root of 1296 ?
1. Write the prime factorization of the number.
­ Write the prime factorization of the number
­ Group the prime factors into pairs
2. Group the prime factors into pairs.
= 2 x 2 x 3 x 3
­ Rearrange the factors into two equal groups
3. Take one number from each group, then multiply ­ Multiply out the two equal groups
1296 = 36
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
What is the square root of 1764 ?
√1764 => 2 x 2 x 3 x 3 x 7 x 7
2 x 3 x 7
42
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Perfect Cube ­ Any whole number that can be represented as the volume
of a cube with a whole number as its edge length.
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216 is a perfect cube!!
6
6
Volume = l x w x h
= 6 x 6 x 6
= 216
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Cube Root ­ A number which, when raised to the exponent 3, results in a given number.
63 = 216, therefore 6 is the cube root of 216
6
6
The edge length of a cube is the cube root of its volume.
6
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Square Root
9
Cube Root
3
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Using Prime Factorization
1. Write the prime factorization of the number.
2. Group the prime factors into sets of 3.
3. Take one number from each group, then multiply.
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
What is the cube root of 1728 ?
3
1. Write the prime factorization of the number.
­ Write the prime factorization of the number
2. Group the prime factors into sets of 3.
­ Group the prime factors into sets of 3
= 2 x 2 x 3
= 12
3
3. Take one number from each group, then multiply.
­ Rearrange the factors into 3 equal groups
­ Multiply out the 3 equal groups
1728 = 12
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
What is the cube root of 2744 ?
∛2744 => 2 x 2 x 2 x 7 x 7 x 7
2 x 7
14
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Page 146
4 a, b
5 b, e
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7a
8a
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Surface Area
Sum of the area
of each face.
Area = L x W
Cube
A cube has
6 equal faces.
Volume = L x W x H
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Volume to surface area
729
∛729 = 3 x 3 x 3 x 3 x 3 x 3 3 x 3
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If the volume of a cube is 729 cm 3 what is the surface area?
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Volume to surface area
∛2744 = 2 x 2 x 2 x 7 x 7 x 7
2 x 7
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If the volume of a cube is 2744 cm3 what is the surface area?
A = L x W
= 14 x 14
= 196 x 6 sides
= 1176
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Surface area to volume
726 = 121
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If the surface area of a cube is 726 cm2 what is the volume?
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
Surface area to volume
2646 = 441
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If the surface area of a cube is 2646 cm2 what is the volume?
√441 = 3 x 3 x 7 x 7
3 x 7
21
441
21
21
V = L x W x H
= 21 x 21 x 21
= 9261
21
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Day 5 ­ 3.2_Perfect_Squares,_Perfect_Cubes,_and_their_Roots (after).notebook
September 13, 2016
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