1. Estimating Irrational Numbers If we know our perfect squares and where they fall on a number line, then how do we estimate our non-perfect squares? Can we estimate where these numbers fall on a number line?

2. WARM UP

3. Perfect Squares  Can you name all of your perfect squares 1 through 20?  Let’s try them (out loud and together)

16. OKAY – Now…… Let’s try the harder ones (they are in order – next time they won’t be)

25. If all perfect squares are RATIONAL … then what are non-perfect squares? These are all rational numbers and can be found easily on a number line

26. What about Non-perfect squares? ALL Non-perfect squares are irrational

27. Estimating  Generally speaking, students have a difficult time estimating…students do not have a fully developed number sense and really don’t get estimating…  The goal of estimating is to get a number that it is close to….we are not looking for an exact number here…the exact number is not important…

28. Estimating using a number line  In the notes section of your notebook draw a number line.  Plot the perfect squares from 1 through 12 on the number line  When estimating the goal is to find out which whole number the perfect square is close to…  That will be your estimate…  Let’s see what it looks like…

29. Number Line  Your number line should look like this…  To find the square root of a number find where it fits on a number line  Then determine the two numbers it fits between  Determine which number it is closest to and look at the perfect square for that number 149162536496481100121144169196225 123456789101112131415 Perfect Squares

30. The estimate of would be 9 Example Find the 149162536496481100121144169196225 123456789101112131415 Perfect Squares The square root of 75 is between the square root of 64 and 81 Since 75 is closer to 81 than 64 the nearest whole number would be 9

31.  In the notes section of your notebook estimate each square root to the nearest whole number 1. 2. 3. Your Turn Solutions 6 12 10

32. Classwork  Let’s work together first…

33. Problem Solving – These are to challenge your thinking….

34. Answer the following problem SHOW WORK! 1.I am a number. I am not zero. If I am squared, I’m still the same number. What number am I? 1

35. Answer the following problem SHOW WORK! 2.If a square bedroom has an area of 144 square feet, what is the length of one wall? 12 feet

36. Answer the following problem SHOW WORK! 3.An artist is making two stained- glass windows. One window has a perimeter of 48 inches. The other window has an area of 110 inches. Which window is bigger? The window with a perimeter of 48 inches.

37. Answer the following problem SHOW WORK! 4.A square garden has an area of 225 square feet. How much fencing will a gardener need to buy in order to place fencing around the garden? 60 feet