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Estimating and approximating square root notes Absent copy Thurs/Fri 3/13,14

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Four steps to approximating square roots Step 1: Find the two sq. roots (perfect squares) that lie below and above the non-perfect square. Then estimate(educated guess) what you think the answer will be. Below Above Ex: ____ ____ What is your estimation of what the sq. root of 11 will be? The square root is closer to so pick something like 3.2. Since the is 3 that is a good guess. Step 2: Divide the radicand (11) by the estimation you came up with and get a quotient (answer). 3.4 11 = 3.2 11 3.2 Step 3: Take the average by adding your (estimate + quotient) 3.2 + 3.4 = 6.6 2 2 2 Step 4: round your answer to the 10ths place. 3.30

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Example 1 Approximate to the 10ths place (use principal root). below above Estimation: Its closer to so 3.7 might be a good answer. Divide: 14 = 3.8 3.7 Average: 3.7 + 3.8 = 7.5 = 3.75 2 2 Round to 10 th place. 3.75 the 7 is in the 10 th place the 5 will round the answer to 3.8 Solution Is this square root a perfect square? YES or NO What is the radicand? The radicand is 14 Step 1: What 2 perfect square does lie between. It lies between the and Is it closer to √9 or √16. Make a educated guess (estimate) on what you think the answer will be. It is closer to the so 3.7 might be good. Step 2: What 2 #’s do I divide to get the quotient? You divide the radicand by you estimate you made. Step 3: How do you get the average after you add your estimate and the quotient? You divide by 2 to get your average. Step 4: What place value do we round the answer too? You round to the nearest 10ths place. 3.8

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Example 2 Approximate to the 10ths place ( use principal root ). below above Estimation: Its closer to so 4.7 might be good answer for the sq. rt. of 22. Divide: 22 = 4.7 4.7 Average: 4.7 + 4.7 = 9.4 4.70 2 2 Round to 10 th place. 4.70 the 7 is in the 10 th place the 0 will keep the 7 in the 10ths place. Solution Is this square root a perfect square? YES or NO What is the radicand? The radicand is 22 Step 1: What 2 perfect square does lie between. It lies between the and Is it closer to √16 or √25. Make a educated guess (estimate) on what you think the answer will be. It is closer to the so 4.7 might be good. Step 2: What 2 #’s do I divide to get the quotient? You divide the radicand by you estimate you made. Step 3: How do you get the average after you add your estimate and the quotient? You divide by 2 to get your average. Step 4: What place value do we round the answer too? You round to the nearest 10ths place. 4.7

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