Using Rational Approximations of Irrational Numbers
Day 1
Objective
I will find rational numbers that approximate irrational numbers.
QOD
What is a square root?
Dow Now
What is the product of 1.18 x 1.18?
Key Terms
ApproximateSquare RootPerfect SquareRadical
Approximateclose to the actual, but not completely accurate or exact.
Square Root
A number that, when multiplied by itself, equals a specific number.
Radical
The root of a number or quantity.
Perfect Squares
The product of a rational number multiplied by itself.
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
Classwork- left side
Find the square root of 5 to one decimal pointAdvanced: to two decimal points
Show all work. Circle the final approximation.
Classwork
Common Core p. 21 #1-3write all questionsshow all work
Exit Ticket
What is a square root?
Day 2
Use Rational Approximations of Irrational Numbers
Objective
I will find rational numbers that approximate irrational numbers.
Do Now
What is the approximate square root of 5?
Key Terms- Quiz Tuesday
ApproximateSquare RootPerfect SquareRadical
Perfect Square
A perfect square is “perfect” because its square root is a whole number.
Example:49 is a perfect square because = 7
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
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
Quick Question 1
I am a number. I am not zero. If I am squared, I’m the same number. What number am I?
Quick Question #2
If a square bedroom has an area of 144 square feet, what is the length of one wall?
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?
Classwork
Exit Ticket
How comfortable are you in preparation for your key terms quiz on Tuesday?
Day 3
Use Rational Approximations of Irrational Numbers
Objective
I will find rational numbers that approximate irrational numbers.
Quiz
Please define the Key Terms below using full and complete sentences.1. Approximate2. Square Root3. Perfect Square4. Radical
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