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