Estimating Square Roots and Cube Roots. Review of Perfect Square Roots.
Square vs. cube
Transcript of 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, 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.
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1 x 1 Square 1x1x1 Cube
One square
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2x2 Square not a Cube
Four Blocks
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3x3 Square not a Cube
Nine Blocks
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4x4 Square not a Cube
16 Blocks
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Write side side 2 side 3
123456789
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Write
side side 2 side 31 1x1=1 1x1x1=12 2x2=4 2x2x2=83 3x3=9 3x3x3=27456789
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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
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5x5 Square not a Cube
25 Blocks
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6x6 Square not a Cube
36 Blocks
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7x7 Square not a Cube
49 Blocks
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8x8 Square 4x4x4 Cube
64 Blocks
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Cube = Square
How many pieces will make a cube and a square?
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Square = 8x8=64
8=2x2x2thus 8x8= (2x2x2) x (2x2x2) 2x2x2x2x2x2= 26
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Cube = 4x4x4=64
4=2x2On the cube: 4x4x4 can be written:(2x2) x (2x2) x (2x2) = 26
82 = 43
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When will it occur again?
1x1x1x1x1x1= 12x2x2x2x2x2= 64????Find the next 4 numbers that are perfect squares and perfect cubes.