Square vs. cube
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WHEN CAN A PERFECT SQUARE MAKE A PERFECT CUBE? Expressions and Equations 8.EE Work with radicals and integer exponents. 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 × 3 –5 = 3 –3 = 1/3 3 = 1/27. 2. Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. 3. Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10 8 and the population of the world as 7 times 10 9 , and determine that the world population is more than 20 times larger. 4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Transcript of Square vs. cube
WHEN CAN A PERFECT SQUARE
MAKE A PERFECT CUBE?Expressions and Equations 8.EE
Work with radicals and integer exponents.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. 2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of
small perfect cubes. Know that √2 is irrational. 3. Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For
example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger. 4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for
measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
1 x 1 Square 1x1x1 Cube
One square
2x2 Square not a Cube
Four Blocks
3x3 Square not a Cube
Nine Blocks
4x4 Square not a Cube
16 Blocks
Write side side 2 side 3
123456789
Write
side side 2 side 31 1x1=1 1x1x1=12 2x2=4 2x2x2=83 3x3=9 3x3x3=27456789
side side 2 side 31 1x1=1 1x1x1=12 2x2=4 2x2x2=83 3x3=9 3x3x3=274 16 645 25 1256 36 2167 49 3438 64 5129 81 72910 100 100011 121 133112 144 172813 169 219714 196 2744
5x5 Square not a Cube
25 Blocks
6x6 Square not a Cube
36 Blocks
7x7 Square not a Cube
49 Blocks
8x8 Square 4x4x4 Cube
64 Blocks
Cube = Square
How many pieces will make a cube and a square?
Square = 8x8=64
8=2x2x2thus 8x8= (2x2x2) x (2x2x2) 2x2x2x2x2x2= 26
Cube = 4x4x4=64
4=2x2On the cube: 4x4x4 can be written:(2x2) x (2x2) x (2x2) = 26
82 = 43
When will it occur again?
1x1x1x1x1x1= 12x2x2x2x2x2= 64????Find the next 4 numbers that are perfect squares and perfect cubes.
