Day 5 ­ 3.2 Perfect Squares, Perfect Cubes (after).notebook
February 15, 2017
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Day 5 ­ 3.2 Perfect Squares, Perfect Cubes (after).notebook
February 15, 2017
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Day 5 ­ 3.2 Perfect Squares, Perfect Cubes (after).notebook
February 15, 2017
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 (after).notebook
5
5
February 15, 2017
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 (after).notebook
February 15, 2017
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 (after).notebook
February 15, 2017
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 (after).notebook
February 15, 2017
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 (after).notebook
February 15, 2017
Perfect Cube ­ Any whole number that can be represented as the volume
of a cube with a whole number as its edge length.
6
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 (after).notebook
February 15, 2017
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 (after).notebook
February 15, 2017
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 (after).notebook
February 15, 2017
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 (after).notebook
February 15, 2017
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 (after).notebook
Square Root
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February 15, 2017
Cube Root
3
8
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Day 5 ­ 3.2 Perfect Squares, Perfect Cubes (after).notebook
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4 a, b
5 b, e
6
7a
8a
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Day 5 ­ 3.2 Perfect Squares, Perfect Cubes (after).notebook
February 15, 2017
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 (after).notebook
Volume to surface area
729
∛729 = 3 x 3 x 3 x 3 x 3 x 3 3 x 3
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February 15, 2017
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 (after).notebook
Volume to surface area
∛2744 = 2 x 2 x 2 x 7 x 7 x 7
2 x 7
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February 15, 2017
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 (after).notebook
Surface area to volume
726 = 121
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February 15, 2017
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 (after).notebook
Surface area to volume
2646 = 441
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February 15, 2017
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 (after).notebook
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