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Estimating and approximating square root notes Absent copy Thurs/Fri 3/13,14 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 16 9 11 ____ Ex: ____ What is your estimation of what the sq. root of 11 will be? The square root is closer to 9 so pick something like 3.2. Since the 9 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 Example 1 • Is this square root a perfect • Approximate to the 10ths place (use principal root). 14 below above 9 16 Estimation: Its closer to 16 so 3.7 might be a good answer. Divide: 14 3.7 = 3.8 Average: 3.7 + 3.8 = 7.5 = 3.75 2 2 Round to 10th place. 3.75 the 7 is in the 10th place the 5 will round the answer to 3.8 3.8 Solution square? YES or NO • What is the radicand? • The radicand is 14 • It lies between the • It is closer to the • You divide the radicand by you estimate you made. • Step 1: What 2 perfect square does 14 lie between. 9 and 16 • Is it closer to √9 or √16. Make a educated guess (estimate) on what you think the answer will be. 16 so 3.7 might be good. • Step 2: What 2 #’s do I divide to get the quotient? • Step 3: How do you get the average after you add your estimate and the quotient? • You divide by 2 to get your average. • You round to the nearest 10ths place. • Step 4: What place value do we round the answer too? Example 2 Approximate to the 10ths • Is this square root a perfect square? YES or NO place (use principal root). • What is the radicand? below 16 Estimation: 22 above 25 Its closer to 25 so 4.7 might be good answer for the sq. rt. of 22. • The radicand is 22 • It lies between the • It is closer to the • Step 1: What 2 perfect square does between. • 22 = 4.7 4.7 • Average: 4.7 + 4.7 = 9.4 4.70 • 2 2 Round to 10th place. 4.7 Solution 25 • Is it closer to √16 or √25. Make a educated guess (estimate) on what you think the answe will be. Divide: 4.70 the 7 is in the 10th place the 0 will keep the 7 in the 10ths place. 16 and 22 lie 25 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 yo add your estimate and the quotient? • You divide by 2 to get your average. • You round to the nearest 10ths place. • Step 4: What place value do we round the answer too?