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Estimating Roots
Lesson 1-9
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Real World Link
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ESTIMATING SQUARE ROOTS TO THE NEAREST TENTH
Once you have found which two whole numbers your square root is between, you must estimate your square root to the nearest tenth.•Decide which whole number your original number is closest to.•Test the square root tenths to find the nearest square to your original number.Example: Estimate √83 to the nearest tenth.
In example 1 we estimated that √83 is between 9 and 10
Since 83 is closer to 81 than 100, we can test tenths close to 9. (9.1)² = 82.81 83.00 – 82.81 = 0.19 (9.2)² = 84.64 84.64 – 83.00 = 1.64
Since (9.1)² is closer to 83, √83 is estimated as 9.1 √83 ≈ 9.2
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ESTIMATE TO THE NEAREST TENTH
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EXAMPLE
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ORDERING NUMBERS To order a set of numbers that include square
roots, you must first estimate the decimal equivalent of the square roots.
Then order the numbers Finally, write the numbers in their original
form. Example: Order the set {7, 9, √50, √85}. 1. Estimate the square roots {7, 9, 7.1, 9.2}
2. Order the decimals {7, 7.1, 9, 9.2} 3. Rewrite in original form {7, √50, 9, √85}
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TRY THESE Estimate to the nearest tenth.
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p 85 #1-31 odd, 32-38 all
HOMEWORK