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Lesson 9-1 Pages 436-440 Squares and Square Roots Read Pages 436-438 PA Lesson Check 7-Ch7 What you will learn! 1. How to find squares and square roots. 2. How to estimate square roots. Perfect Square Square root Radical sign What you really need to know! A perfect square is the square of a whole number. A square root of a number is one of two equal factors of the number. What you really need to know! Every positive number has a positive square root and a negative square root. The square root of a negative number such as –25, is not real because the square of a number is never negative. Square Square Root Example 1: Find the square root: 64 Since 2 8 = 64, 64 8 Example 1b: Find the square root: 121 Since 2 11 = 121, 121 11 Example 1c: Find the square root: 4 Since 2 2 = 4 and 2 (-2) = 4, 4 2 and 2 Example 2: Use a calculator to fine the square root to the nearest tenth. 23 23 4.79583152331271 4.8 Example 2b: Use a calculator to fine the square root to the nearest tenth. 46 46 6.78232998312527 -6.8 Example 3: Estimate the square root to the nearest whole number. 22 The perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, ... 22 is between 16 and 25. 16 4 and 25 5 22 The perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, ... 22 is closer to 25. So 5 is the best estimate for the square root of 22. 22 5 The perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, ... Example 3b: Estimate the square root to the nearest whole number. 319 The perfect squares are: ..., 169, 196, 225, 256, 289, 324, 361, ... 319 is between 289 and 324. 289 17 and 324 18 319 The perfect squares are: ..., 169, 196, 225, 256, 289, 324, 361, ... 319 is closer to 325. So 18 is the best estimate for the square root of 319. 319 18 The perfect squares are: ..., 169, 196, 225, 256, 289, 324, 361, ... Example 4: To estimate how far you can see from a point above the horizon, you can use the formula: D 1.22 A where D is the distance in miles and A is the altitude, or height, in feet. Example 4: The observations deck at the Seattle Space Needle is 520 feet above the ground. On a clear day, about how far could a tourist see? Round to the nearest tenth. D 1.22 A D 1.22 A D 1.22 520 D 1.22 22.8035085019828 D 27.820280372419 D 27.8mi Page 438 Guided Practice #’s 4-11 Read: Pages 436-438 with someone at home and study examples! Homework: Pages 439-440 #’s 12-56 even, 71-80 Lesson Check 9-1 Homework: Pages 439-440 #’s 12-56 even #’s 59, 60 and 71-74 Page 745 Lesson 9-1 Lesson Check 9-1