4 7 Estimating Square Roots Preview Evaluating Algebraic

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

4 -7 Estimating Square Roots Evaluating Algebraic Expressions Warm Up Find the two square roots of each number. 1. 144 ± 12 2. 256 ± 16 Evaluate each expression. 3. 8 + 144 20 4. 7 289 119

4 -7 Estimating Square Roots California Evaluating Algebraic Expressions Standards NS 2. 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.

4 -7 Estimating Square Roots Additional Example 1: Estimating Square Roots of Numbers The. Evaluating 55 is between two integers. Name the Algebraic Expressions integers. Explain your answer. 55 36, 49, 64, 81 List perfect squares near 55. 49 < 55 < 64 Find the perfect squares nearest 55. 49 < 55 < 64 Find the square roots of the perfect squares. 7 < 55 < 8 55 is between 7 and 8 because 55 is between 49 and 64.

4 -7 Estimating Square Roots Check It Out! Example 1 The 80 is between two integers. Name the Evaluating Algebraic Expressions integers. Explain your answer. 80 49, 64, 81, 100 List perfect squares near 80. 64 < 80 < 81 Find the perfect squares nearest 80. 64 < 80 < 81 Find the square roots of the perfect squares. 8 < 80 < 9 80 is between 8 and 9 because 80 is between 64 and 81.

4 -7 Estimating Square Roots Additional Example 2: Recreation Application A Coast Guard boat searching for a lost sailboat covers a square area of 185 mi 2 Expressions. What is the Evaluating Algebraic approximate length of each side of the square area? Round your answer to the nearest mile. The length of each side of the square is √ 185. 144, 169, 196, 225 List perfect squares near 185. 169 < 185 < 196 Find the perfect squares nearest 185. √ 169 < √ 185 < √ 196 Find the square roots of the perfect squares. 13 < √ 185 < 14 185 is closer to 196 than to 169, so √ 185 14 185 is closer to 14 than 13. Each side of the search area is about 14 miles long.

4 -7 Estimating Square Roots Check It Out! Example 2 A tent was advertised in the newspaper as having 2. What is the an enclosed square area of 168 ft Evaluating Algebraic Expressions 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. near 168. 121, 144, 169, 196 List perfect squares 144 < 168 < 169 Find the perfect squares nearest 168. √ 144 < √ 168 < √ 169 Find the square roots of the perfect squares. 12 < √ 16 < 13 8 168 is closer to 169 than to 144, so √ 168 13 168 is closer to 13 than 12. Each side of the tent is about 13 feet long.

4 -7 Estimating Square Roots Additional Example 3: Approximating Square Roots to the Nearest Hundredth Evaluating Expressions Approximate √ 135 Algebraic to the nearest hundredth. Step 1 Find the value of the whole number. 121 < 135 < 144 Find the perfect squares nearest 135. √ 121 < √ 135 <√ 144 Find the square roots of the perfect squares. 11 < √ 135 < 12 The number will be between 11 and 12. The whole number part of the answer is 11.

4 -7 Estimating Square Roots Additional Example 3 Continued Approximate √ 135 Algebraic to the nearest hundredth. Evaluating Expressions Step 2 Find the value of the decimal. Find the difference between the 135 – 121 = 14 given number, 135, and the lower perfect square. Find the difference between the 144 – 121 = 23 greater perfect square and the lower perfect square. 14 Write the difference as a ratio. 23 Divide to find the approximate 14 ÷ 23 ≈ 0. 609 decimal value.

4 -7 Estimating Square Roots Additional Example 3 Continued Approximate √ 135 Algebraic to the nearest hundredth. Evaluating Expressions Step 3 Find the approximate value. 11 + 0. 609 = 11. 609 Combine the whole number and decimal. 11. 609 ≈ 11. 61 Round to the nearest hundredth. The approximate value of is 11. 61. 135 to the nearest hundredth

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

4 -7 Estimating Square Roots Check It Out! Example 3 Continued Approximate √ 180 Algebraic to the nearest hundredth. Evaluating Expressions Step 2 Find the value of the decimal. Find the difference between the 180 – 169 = 11 given number, 180, and the lower perfect square. Find the difference between the 196 – 169 = 27 greater perfect square and the lower perfect square. 11 Write the difference as a ratio. 27 Divide to find the approximate 11 ÷ 27 ≈ 0. 407 decimal value.

4 -7 Estimating Square Roots Check It Out! Example 3 Continued Approximate √ 180 Algebraic to the nearest hundredth. Evaluating Expressions Step 3 Find the approximate value. 13 + 0. 407 = 13. 407 Combine the whole number and decimal. 13. 407 ≈ 13. 41 Round to the nearest hundredth. The approximate value of is 13. 41. 180 to the nearest hundredth

4 -7 Estimating Square Roots Additional Example 4: Using a Calculator to Estimate the Value of a Square Root Evaluating Algebraic Expressions Use a calculator to find the nearest tenth. 600. Round to 600 ≈ 24. 494897… Use a calculator. 600 ≈ 24. 5 Round to the nearest tenth. 600 rounded to the nearest tenth is 24. 5.

4 -7 Estimating Square Roots Check It Out! Example 4 Evaluating Algebraic Expressions Use a calculator to find the nearest tenth. 800. Round to 800 ≈ 28. 28427125… Use a calculator. 800 ≈ 28. 3 Round to the nearest tenth. 800 rounded to the nearest tenth is 28. 3.

4 -7 Estimating Square Roots Lesson Quiz Each square root is between two integers. Name the integers. Evaluating Algebraic Expressions 1. 27 5 and 6 3. Approximate 13. 75 2. 456 21 and 22 189 to the nearest hundredth. 4. Use a calculator 34. 9 to find 1219. 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. 12 ft