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Using Rational Approximations of Irrational Numbers
Day 1
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Objective
I will find rational numbers that approximate irrational numbers.
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QOD
What is a square root?
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Dow Now
What is the product of 1.18 x 1.18?
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Key Terms
ApproximateSquare RootPerfect SquareRadical
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Approximateclose to the actual, but not completely accurate or exact.
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Square Root
A number that, when multiplied by itself, equals a specific number.
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Radical
The root of a number or quantity.
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Perfect Squares
The product of a rational number multiplied by itself.
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How to approximate the side length of a square with the are 2 feet squared
Remember, the formula for the area of a square is A=s^2
1. You know that 1^2=1 and 2^2= 4a. the side length must be between 1 and 2b. guess & check
i. try 1.5 (2.25), 1.3 (1.69), 1.4 (1.96)ii. the answer is probably closer to 1.4
1. try 1.21 (1.9881), 1.42 (2.0164 too big), 1.415 (2.002225)
2. because 2.002225 > 2, s must be less than 1.415. To the nearest hundredth
iii. Our estimate is 1.41 feet
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Classwork- left side
Find the square root of 5 to one decimal pointAdvanced: to two decimal points
Show all work. Circle the final approximation.
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Classwork
Common Core p. 21 #1-3write all questionsshow all work
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Exit Ticket
What is a square root?
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Day 2
Use Rational Approximations of Irrational Numbers
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Objective
I will find rational numbers that approximate irrational numbers.
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Do Now
What is the approximate square root of 5?
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Key Terms- Quiz Tuesday
ApproximateSquare RootPerfect SquareRadical
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Perfect Square
A perfect square is “perfect” because its square root is a whole number.
Example:49 is a perfect square because = 7
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Non-Perfect Squares
A non-perfect square: is a number whose square root is NOT a whole number.
Example:40 is NOT a perfect square because = 6.2345
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Approximating Square RootsYou need to estimate its value of non-perfect squares by determining which two perfect squares it falls in between.
Example:11 is a non-perfect square11 falls between perfect squares 9 & 16Therefore, square root of 11 is between the square root of 9 and the square root of 16SO the square root is between 3 & 4
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Quick Question 1
I am a number. I am not zero. If I am squared, I’m the same number. What number am I?
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Quick Question #2
If a square bedroom has an area of 144 square feet, what is the length of one wall?
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Quick Question #3
An artist is making two stained-glass windows. One window has a perimeter of 48 inches. The others window has an area of 110 inches. Which window was bigger?
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Classwork
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Exit Ticket
How comfortable are you in preparation for your key terms quiz on Tuesday?
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Day 3
Use Rational Approximations of Irrational Numbers
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Objective
I will find rational numbers that approximate irrational numbers.
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Quiz
Please define the Key Terms below using full and complete sentences.1. Approximate2. Square Root3. Perfect Square4. Radical