P.O.D. #38 Using the formula: a² + b² = c² Determine whether each triangle with sides of given lengths is a right triangle. Justify your answer. 1.) 7 cm, 14 cm, 16 cm 2.) 40 m, 42 m, 58 m 3.) 24 in., 32 in., 38 in. 4.) 15 mm, 18 mm, 24 mm Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary. 5.) How high will the ladder reach? 6.) How far is the bear from camp?

P.O.D. #38 Answers: 1.) no 2.) yes 3.) no 4.) no 5.) h² + 4² = 16² 6.) 20² + d² = 60² h = 15.5ft d = 56.6yd

Module 7 Lesson 2 OUTCOME Students know that √n means “the square root of n”, that n is not always a perfect square, and that they can approximate the location of square roots on the number line.

M7L2 Discussion What is a perfect square? A number (n) times itself. Examples: 1² = 1 2² = 4 3² = 9 4² = 16, etc. So when we see this: √16 = ? We know that 4 is square root of √16 because 4² = 16

M7L2 Discussion What do we do when we need to find the square root of a non-negative number (n) “√n” when n is not a perfect square? Examples: √2, √14, √150

M7L2 Notes When finding the square root of a number that does not have a perfect square: Find the nearest perfect squares on either side of that number. Example: √14 We know these perfect squares: √9 = 3 and that √16 = 4 So we know that 3 < √14 < 4

M7L2 Notes Since we know 3 < √14 < 4 We need to determine if √14 is closer to 3 or if it is closer to 4. Start with a number line: This number line already has the square roots of: √1, √4, √9, and √16.

M7L2 Notes Write these square roots on the number line: We know that, since the numbers 2 and 3 follow 1 and come before 4, we can also know that √2 and √3 follow √1 and come before √4.

M7L2 Notes Now fill in the rest of the square roots: We see on the number line that the √14 is closer to 4 than to 3. In fact, it is between 3.5 and 4. You can guess and check until you come closer to the actual number. (Or use your handy-dandy calculator.)

M7L2 Exercises 1-9

M7L2 HOMEWORK Page S. 10, # 1-7 ODD only