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Lesson 1.4 Estimating Square Roots.notebook Sec 1.4 September 24, 2012 Estimating Square Roots 2. If the side length of a square is 4 cm, what is the area of the square? Pages 22-27. First, some quick review. 1. If the area of a square is 36 cm2 , what is the side length of the square? 4cm Area 4cm ? 36cm2 side length = = length x length = 4cm x 4cm = 16cm2 ? = ? Aug 276:58 PM Aug 277:04 PM Estimating Square Roots that are non-perfect. 3. If the area of a square is 30 cm2, what is the side length of the square? A non-perfect square is a number that cannot be written as a product of two equal numbers. In the next example 30 is a non-perfect square. Perfect 9 Perfect 25 Non-perfect 30 Aug 276:58 PM Perfect Squares 1 Between which two consecutive perfect 4 squares does 30 fall ? 9 16 25 30 is halfway between 25 36 and 36 so answer is about 5.5 49 64 81 100 121 This is the perfect square method of 144 approximating a square root for a 169 non-perfect square. 196 225 . . . etc 25 = 5 36 = 6 Sep 1411:23 PM ? 30cm2 side length = = ??? ? This is not a perfect square so we can‛t get an exact answer. But we can estimate using the perfect squares we do know. Aug 277:07 PM Now, let's use the Numberline Method to find square roots that are not perfect. First we draw a number line and record the perfect square less than our number and the perfect square more than our number. For 30 the perfect square below is 25 and the perfect square above is 36. Sep 1411:31 PM 1 Lesson 1.4 Estimating Square Roots.notebook September 24, 2012 Example 2: Use the number line method to show the estimated value of each square root. 25 36 5 5.5 is 5 away from 6 a) 10 3 41 b) 4 c) 5 31 d) 56 6 7 8 and 6 away from Since these numbers are almost the same distance away, would be close to the middle of these two numbers. Since is closer to we can say is approximately 5.4. Sep 1411:44 PM Example 3: Is the whole number less than, equal to or greater than the given square root? Aug 277:16 PM Example 4: Which whole number is closest to? a) 5 or b) 9 or Sep 1512:26 AM Example 5: What is the approximate side length of a square with an area of 56 cm ? Give the answer to one decimal place. Use a calculator. Sep 239:54 PM Prime Factorization to estimate square root 1. Factor the number into prime factors 2. Combine pairs 3. Multiply ONE from each pair together to get answer. So, 36 = 6 Sep 239:58 PM Sep 1512:33 AM 2 Lesson 1.4 Estimating Square Roots.notebook Do this one: 1. Factor the number into prime factors 2. Combine pairs 3. Multiply ONE from each pair together to get answer. Sep 1512:38 AM September 24, 2012 Complete questions on pages 2527: #'s 4 , 5 and 7 a) with class. Assign 7 b, 8 a, 8 b, and 8 d for seatwork. Homework: Use your calculator to estimate square roots in # 12, 13, 16, 17. Now you can estimate square roots using: 1. Blocks or grid paper 2. Perfect squares 3. Number lines 4. Calculator or 5. Prime factors (Factoring & combining pairs) Sep 1411:18 PM 3