Download math 1201 3.2.notebook

math 1201 3.2.notebook
October 19, 2015
3.2­ Perfect Squares,
Perfect Cubes, and Their Roots.
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math 1201 3.2.notebook
October 19, 2015
A perfect square is any whole number that can be expressed as the product of two equal integers.
Examples:
A perfect square is a number that can be represent the area of a
square with a whole number as the side length.
Examples:
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math 1201 3.2.notebook
October 19, 2015
The side length of the square is the square root of the area of the square.
There are a few ways to determine if a number is a square number,
and to find its square root:
1 – Estimate the value of root and then guess and check
2 – Use Prime factorization with grouping
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math 1201 3.2.notebook
October 19, 2015
Estimate the value of root and then guess and check
Determine whether 361 is a perfect square.
Estimate what this root is.
Find two perfect squares that this number lies between.
100 < 361 < 400
102 < 361 < 202
This means the square root of 361 should lie between 10 and 20.
Is it close to 10 or to 20?
Try squaring some numbers close to 20.
(IF you get 361 then 361 is a perfect square and the number you squared is the square root of 361)
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math 1201 3.2.notebook
October 19, 2015
Example 2 – Determine if 576 is a square number
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math 1201 3.2.notebook
October 19, 2015
Use Prime factorization with grouping
We can also use the prime factorization of a number to
determine if a number is a square number, and calculate the
square root.
If the prime factors of a number can be paired together then
the number is a perfect square
The square root of the number is equal to the product of the
factors in each pair.
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math 1201 3.2.notebook
October 19, 2015
Example 3 – Determine if 36 is a square number using prime factorization and find it’s square root if possible.
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math 1201 3.2.notebook
October 19, 2015
Example 4 – Determine if 524 is a square number using prime factorization and find it’s square root if possible.
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math 1201 3.2.notebook
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Example 5 – Determine if 11025 is a square number using its prime factorization, and find it’s square root if possible.
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math 1201 3.2.notebook
October 19, 2015
Example 6 – Determine if 1200 is a square number using its prime factorization, and find it’s square root if possible.
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math 1201 3.2.notebook
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CUBES
A perfect cube is any whole number that can be expressed as
the product of three equal integers .
A perfect cube is any number that can be represented as the
volume of a cube with a whole number as the edge length.
The edge length of the cube is the cube root of the number.
We use to denote the cube root.
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math 1201 3.2.notebook
October 19, 2015
There are a few methods to find determine the cube root of a number and to find a cube root.
1 – Use linking cubes to make a large cube with a given number of linking cubes (small numbers).
2 – Use guess and check (not recommended)
3 – Use the prime factorization of the number to see if it can be
organized into three equal groups.
(The cube root is equal to the product of one group.)
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math 1201 3.2.notebook
October 19, 2015
Example 7: Determine the cube root of 2744.
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math 1201 3.2.notebook
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Example 8: Determine the cube root of 13824.
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math 1201 3.2.notebook
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Example 9: A cube has the volume of 12 167cm3 what is the surface area of the cube?
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math 1201 3.2.notebook
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Please Complete: Pg146 # 4e,5e,
6ace,7a,8a,10,11
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