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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Warm Up Find the two square roots of each number. Evaluate each expression

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots NS2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not a square, determine without a calculator the two integers between which its square root lies and explain why. California Standards

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Additional 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 Check It Out! Example 1 List perfect squares near 80.49, 64, 81, < 80 < 81 Find the square roots of the perfect squares is between 8 and 9 because 80 is between 64 and 81. The 80 is between two integers. Name the integers. Explain your answer. Find the perfect squares nearest < 80 < 81 8 < 80 < 9

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots A Coast Guard boat searching for a lost sailboat covers a square area of 185 mi 2. What is the approximate length of each side of the square area? Round your answer to the nearest mile. Additional Example 2: Recreation Application 169 < 185 < 196 Find the perfect squares nearest 185. Find the square roots of the perfect squares. Each side of the search area is about 14 miles long. The length of each side of the square is 185. < < < < , 169, 196, 225 List perfect squares near is closer to 196 than to 169, so 185 is closer to 14 than 13.

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Check It Out! Example 2 A tent was advertised in the newspaper as having an enclosed square area of 168 ft 2. What is the approximate length of the sides of the square area? Round your answer to the nearest foot. The length of each side of the square is < 168 < 169Find the perfect squares nearest 168. Find the square roots of the perfect squares. < < < < Each side of the tent is about 13 feet long. 121, 144, 169, 196 List perfect squares near is closer to 169 than to 144, so 168 is closer to 13 than 12.

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Additional Example 3: 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 < < 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 Additional Example 3 Continued 135 – 121 = ÷ 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 Additional Example 3 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 Check It Out! Example < 180 < 196 The whole number part of the answer is 13. Find the perfect squares nearest 180. Find the square roots of the perfect squares. 169 < 180 < < 180< 14 Step 1 Find the value of the whole number. The number will be between 13 and 14. Approximate 180 to the nearest hundredth.

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Check It Out! Example 3 Continued 180 – 169 = ÷ Find the difference between the given number, 180, and the lower perfect square. Step 2 Find the value of the decimal. Write the difference as a ratio. 196 – 169 = 27 Find the difference between the greater perfect square and the lower perfect square Divide to find the approximate decimal value. Approximate 180 to the nearest hundredth.

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Check It Out! Example 3 Continued = Combine the whole number and decimal. Step 3 Find the approximate value Round to the nearest hundredth. The approximate value of 180 to the nearest hundredth is Approximate 180 to the nearest hundredth.

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

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Check It Out! Example … Use a calculator to find 800. Round to the nearest tenth. Use a calculator. Round to the nearest tenth. 800 rounded to the nearest tenth is 28.3.

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Evaluating Algebraic Expressions 4-7 Estimating Square Roots Lesson Quiz Each square root is between two integers. Name the integers Approximate 189 to the nearest hundredth. 4. Use a calculator to find Round to the nearest tenth. 5. A square room requires 154 ft 2 of wall-to-wall carpeting to cover the floor. What is the length of each side of the room? Round your answer to the nearest foot. 5 and 621 and ft

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