Find the two square roots of each number. Warm Up Find the two square roots of each number. Evaluate each expression. 1. 144 2. 256 12 16 3. 8+ 144 4. 7 289 20 119

Example 1: Estimating Square Roots of Numbers The square root is between two integers. Name the integers. Explain your answer. Think: What are perfect squares close to 55? Think: What are perfect squares close to 90? A. 55 – B. 90 (–9)2 = 81 72 = 49 81 < 90 49 < 55 82 = 64 64 > 55 (–10)2 = 100 100 > 90     2

Example 1: Estimating Square Roots of Numbers The square root is between two integers. Name the integers. Explain your answer. C. D. Think: What are perfect squares close to 80? – Think: What are perfect squares close to 45? 80 45 82 = 64 64 < 80 (–6)2 = 36 36 < 45 92 = 81 81 > 80 (–7)2 = 49 49 > 45     3

Example 2: Application You want to sew a fringe on a square tablecloth with an area of 500 square inches. Calculate the length of each side of the tablecloth and the length of fringe you will need to the nearest tenth of an inch. The length of each side of the square is √500 . 484 < 500 < 529 The length of each side of the table is about 22.4 in., and you will need about 89.6 in. of fringe.

Check It Out: Example 2 A tent was advertised in the newspaper as having an enclosed square area of 168 ft2. 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 √168 144 < 168 < 169 < √168 √144 √169 12 < < 13 √168 √168  13 feet

Example 3: Approximating Square Roots to the Nearest Hundredth Approximate to the nearest hundredth. Step 1: Find the value of the whole number. 121 < 141 < 144 whole number part  11 Step 2: Find the value of the decimal. Find the difference between the given number, 141, and the lower perfect square. 141 – 121 = 20 Find the difference between the greater perfect square and the lower perfect square. 144 – 121 = 23 20 23 Write the difference as a ratio. ≈ 0.869 Divide to find the approximate decimal value. Step 3: Find the approximate value. 11 + 0.869 = 11.869 ≈ 11.87

Example 4: Using a Calculator to Estimate the Value of a Square Root Use a calculator to find 600. Round to the nearest tenth. Using a calculator, 600 ≈ 24.49489742…. Rounded, 600 is 24.5. 7

Each square root is between two integers. Name the two integers. Lesson Quiz Each square root is between two integers. Name the two integers. 1. 27 2. – 456 5 and 6 –22 and –21 Use a calculator to find each value. Round to the nearest tenth. 3. 89 4. 1223 9.4 35.0 5. A square field has an area of 2000 square feet. To the nearest foot, how much fencing would be needed to enclose the field? 179 ft 8