Perfect Squares & Square Roots - Weebly€¦ · Ie. 8 8 5 4 4 5 8 8 5 4 4 7 : 6 9 36 & 25 are...
Transcript of Perfect Squares & Square Roots - Weebly€¦ · Ie. 8 8 5 4 4 5 8 8 5 4 4 7 : 6 9 36 & 25 are...
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Perfect Squares & Square Roots A Connection to Rational & Irrational Numbers
Math 9 – Mrs. Feldes
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A Perfect square is the result of squaring a number.
Each perfect square forms a square.
Review:
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Squaring & square root are inverse operations!
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So far, you have studied whole number perfect squares.
Such as:
1,4,9,16,25,36,49,64,81,100,121,,
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Specifically, the result of a whole number perfect square wouldfit in as a Natural or Whole.
Ie.
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Perfect squares can be also be FRACTIONS!
Perfect Squares:
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Ie. is a perfect square since
A Perfect square is the result of squaring ANY number, including fractions!
Perfect Squares:
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A perfect square fraction in simplest form must have a perfect square in the numerator ANDdenominator.
Ie. is a perfect square since 16 & 25 are both perfect squares!
Perfect Squares:
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1 Unit
Pictorially, would represent a square with an area of 25 with 16 of them shaded.
Perfect Squares:
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The result of the square root would be the full side length in relation to the shaded squares.
1 Unit
Perfect Squares:
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Perfect squares can be also be DECIMALS!
This is true since decimals & fractions can interchange.
Perfect Squares:
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Ie. 36 & 25 are
perfect squares
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A terminating decimal in fraction form has a power of 10 in the denominator that matches the number of decimal places.
Therefore, is a perfect square!
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Some repeating decimals as a fraction will have a 9,99,999,… in the denominator to match the number of digits that repeat.
Ie. 1 & 9 are perfect squares
Therefore, is a perfect square!
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PERFECT SQUARES POWER OF 10
100
10,000
1,000,000
Powers of 10 with an even exponent or with an even number of zeros are perfect squares!
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Perfect squares exists as many different types of numbers:
1,4,9,16,25,36,49,64,81,100,121,144,
, , , , , , , , , , , ,…
…
CONCLUSION:
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Ie.
CONCLUSION:
Now the best placement would fit in as a Rational Number.