Natural Whole Integer Rational Irrational Real. Sep 8 6:51 AM. Today we are starting our first non review unit REAL NUMBERS
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1 Warm Up: 1. Prove that 0.14 can be written as a fraction 2. Mark a check in each column that idenfies the subset of the Real number system to which the number belongs. Natural Whole Integer Rational Irrational Real. 4. Sep 8 6:51 AM Today we are starting our first non review unit REAL NUMBERS We will start with Squares, Roots, and Estimating Roots Sep 8 7:00 AM 1
2 Sep 5 11:50 AM Sep 5 11:5 AM 2
3 Notation: To indicate a square root, we use a radical sign The number inside the radical sign is called the radicand RADICAL 16 RADICAND Sep 5 11:54 AM The radicand (or number inside the radical) is the number that you are finding the square root of. Example: 25 This is read as "the Square Root of 25" 25 = 5 This is read as "the Square Root of 25 is 5" 25 = 5 This means that 5 2 (or 5 x 5) equals 25 Sep 5 11:56 AM
4 Integer Integer 2 Square Root Sep 5 1:0 PM NOTE: Each perfect square has two square roots... one positive and one negative Why is that? Discuss... Sep 5 12:01 PM 4
5 25 = 5 and 5 Because 5 x 5 = 25 AND 5 x 5 = 25 Notation: We can indicate the square root of 25 is positive or negative 5 like this: 5 Sep 5 12:0 PM Let's try a few together... * If a negative is inside the radical sign, it has no solution! Sep 5 12:06 PM 5
6 Work on the following: Sep 5 12:14 PM How could we figure out a square root or cube root of a non perfect square or non perfect cube without a calculator? "What 2 whole numbers does this root fall between?" Sep 5 1:08 PM 6
7 Sep 5 12:16 PM TRICK FOR ESTIMATING SQUARE ROOTS!!!! The first step is to find the the next smallest and next largest perfect squares that your number lies between. In this example, we need to know that 97 lies between 81 and 100. Since 81 = 9*9 and 100 = 10*10, we can deduce that the square root of 97 is between 9 and 10. We are going to estimate the square root as a proper fraction of the form 9 + x/y, where the numerator x is smaller than the denominator y. Next, find the difference between your number and the next smallest square. In this case, the difference between 97 and 81 is 16. This is going to be the numerator x. Now find the difference between the two perfect squares. In this example, = 19. This is going to be the denominator y. Putting everything together, we can estimate the square root of 97 as 9 and 16/19. As a decimal, this is approximately The actual square root of 97 is approximately This method always yields an estimate that is slightly less than the true value, but the larger the number you start with, the better the estimate. Let's Try!! 16 = = 5 Sep 5 1:09 PM 7
8 Sep 16 1:20 PM Sep 16 12:07 PM 8
9 Sep 9 :55 PM estimate the following square roots Sep 5 1:00 PM 9
10 Sep 9 12:5 PM Sep 9 12:5 PM 10
11 Sep 9 12:5 PM Word Problem: Mrs Draper wants to build a small garden in her back yard. She decided that in order to hold all the vegetable and flower plants she wants, she needs the garden to be 50 square feet. Her husband says he will cut wooden planks to box off her garden but he needs to know how much wood to cut. If she wants her garden to be in the shape of a square, about how long will each side be? Sep 5 1:10 PM 11
12 Work on the following with your table... Sep 9 7:52 AM Ticket Out the Door 1. Work with a partner: Write the following real numbers in ascending order. Show all of your work to jusfy your reasoning. 2.,, 0.45,,, Describe the value of the numbers in the set? a. They are less than 6 b. They are between 6 and 7 c. They are inclusive of 6 and 7 d. They are between 5 and 6 Sep 15 8:28 PM 12
13 . On a number line, let S represent the largest integer value that is less than. Let T represent the largest integer value that is less than. What is the distance between S and T? 4. Sep 15 8:9 PM Sep 15 8:45 PM 1
14 Sep 5 12:07 PM Notation: To indicate a square root, we use a sign very similar to the radical sign... it looks like this: 27 What is different about this sign? What indicator is significant in knowing that it is a "cube root" not a square root? The number inside the radical sign is what you are finding the cube root of. Sep 5 12:08 PM 14
15 Integer Integer Cube Root Sep 5 1:0 PM Sep 9 11:29 AM 15
16 Sep 9 :2 PM Sep 9 11: AM 16
17 Sep 9 :22 PM Sep 9 :19 PM 17
18 Warm Up: Are the following perfect squares? If so, what are their roots? a. 121 b. 144 c. 48 Are the following perfect cubes? If so, what are their roots? d. 512 e. 11 f. 124 Sep 9 7:09 AM Sep 9 7:5 AM 18
19 Sep 9 7:54 AM Sep 9 7:54 AM 19
20 Roots_and_Estimating[1].notebook PAUSE!!! Let's take a minute to learn how to find square roots and cube roots on the calculator... Sep 5 12:09 PM 1. Hit the "2nd" button 2. Hit the "x2" button. Type the number you want to find the square root of 4. Hit "ENTER" Sep 8 7:11 AM 20
![Roots_and_Estimating[1].notebook 1. Hit the "MATH" button 2. Hit "4".](/docs-images/72/67258916/images/21-1.jpg "Type the number you want to find the cube root for 4.")
21 Roots_and_Estimating[1].notebook 1. Hit the "MATH" button 2. Hit "4". Type the number you want to find the cube root for 4. Hit "ENTER" Sep 5 12:11 PM Sep 9 :0 PM 21
Working with Square Roots. Return to Table of Contents
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