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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Math fact: The sum of any number of consecutive odd whole numbers, beginning with 1, is a perfect square e.g. 1+3=4, 1+3+5=9, =16

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Example 1: Estimating Square Roots of Numbers The 55 is between two integers. Name the integers. Explain your answer. List perfect squares near 55.36, 49, 64, < 55 < 64 Find the square roots of the perfect squares is between 7 and 8 because 55 is between 49 and 64. Find the perfect squares nearest < 55 < 64 7 < 55 < 8

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Example 2: Approximating Square Roots to the Nearest Hundredth 121 < 135 < 144 The whole number part of the answer is 11. Find the perfect squares nearest 135. Find the square roots of the perfect squares. √121 < √135 < 144 √ 11 < 135< 12 √ Step 1 Find the value of the whole number. The number will be between 11 and 12. Approximate √135 to the nearest hundredth.

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Example 2 Continued 135 – 121 = ÷ 23 ≈ Find the difference between the given number, 135, and the lower perfect square. Approximate √135 to the nearest hundredth. Step 2 Find the value of the decimal. Write the difference as a ratio. 144 – 121 = 23 Find the difference between the greater perfect square and the lower perfect square Divide to find the approximate decimal value.

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Example 2 Continued = Combine the whole number and decimal. Step 3 Find the approximate value ≈ Round to the nearest hundredth. The approximate value of 135 to the nearest hundredth is Approximate √135 to the nearest hundredth.

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Example 3: Using a Calculator to Estimate the Value of a Square Root Use a calculator to find 600. Round to the nearest tenth. 600 ≈ ≈ … Use a calculator. Round to the nearest tenth. 600 rounded to the nearest tenth is 24.5.

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