May 2 nd May 6 th. Unit 10: Rational & Irrational Numbers
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1 Math 8: Week 33 Math Packet May 2 nd May 6 th Unit 10: Rational & Irrational Numbers
2 Jump Start Directions: Fill out all the BINGO boards on pages 1-2 with the following perfect square numbers: 2, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. You will have to repeat some number and there is no free space. Game 1: Regular BINGO 1
3 Game 2: Four Corners Game 3: Cover All 2
4 Square Roots Recall: Perfect squares and square roots are opposites. So since 3 2 = 9 then 9 = 3. What would be another perfect square and its corresponding square root? Example 1: Determine the positive square root of 81, if it exists. Explain. Example 2: Determine the positive square root of 225, if it exists. Explain. Example 3: Determine the positive square root of 36, if it exists. Explain. Example 4: Determine the positive square root of 49, if it exists. Explain. Example 5: Place the numbers 1, 4, 9, 16. Example 6: Using the number line from Example 5, place the numbers 2 and 3 on the number line. 3
5 Number: a number that can be written as a whole number, fraction, or decimal that terminates (ends) or repeats. Examples: Number: a decimal number that continues on forever without terminating (ending) or repeating Examples: Practice Questions Directions: Determine the positive square root of the number given. If the number is not a perfect square, determine what square root it would be closest to, then give an approximate answer to one or two decimal places using your calculator. 1) 49 2) 62 3) 122 4) 400 5) Which of the numbers in Exercises 1 4 are not perfect squares? Explain. 6) Circle the numbers in Exercises 1-4 that are rational. Explain how you knew what numbers to circle. 4
6 7) Place the following numbers on the number line below: 16, 9, 11, ) Write the positive square root of a number x in symbolic notation. Monday Exit Ticket 1) On our scale of 0-5, rank how well you understand perfect squares and square roots before completing problems ) Determine the positive square root of 196, if it exists. Explain. 3) Determine the positive square root of 50, if it exists. Explain. 4) Using the numbers 196 and 50, identify which is rational and which is irrational. Justify your answer. 5
7 Jump Start Directions: The numbers in each column are related. Your goal is to determine how they are related, determine which numbers belong in the blank parts of the columns, and write an explanation for how you know the numbers belong there. Find the Rule Part 1 Find the Rule Part 2 6
8 Equations with Square and Cube Roots Example 1: x 2 = 25 a) Explain the first step in solving this equation. b) Solve the equation and check your answer. Example 2: x 2 = 25-1 a) Recall: 25-1 can be rewritten as... b) Solve the equation and check your answer. Example 3: x 3 = 8 a) Explain the first step in solving this equation. b) Solve the equation and check your answer. 7
9 Practice Questions 1) =169 a) Explain the first step in solving this equation. b) Solve the equation and check your answer. 2) A square-shaped park has an area of 324 ft 2. What are the dimensions of the park? Write and solve an equation. 3) 625= 4) A cube has a volume of 27 in 3. What is the measure of one of its sides? Write and solve an equation. 8
10 5) What positive value of makes the following equation true: =64? Explain. 6) What positive value of makes the following equation true: =64? Explain. 7) =256 Find the positive value of x that makes the equation true. 8) =343 Find the positive value of x that makes the equation true. 9) Is 6 a solution to the equation 4=5? Explain why or why not. 10) What positive value of would make the following equation true: 19+ =68? 9
11 Jump Start Directions: Answer each question below. 1) a) What does 16 equal? 2) a) What does 36 equal? b) What does 4 4 equal? b) What does 6 6 equal? c) Does 16= 4 4? c) Does 36= 6 6? 3) a) What does 121 equal? 4) a) What does 81 equal? b) What does equal? b) What does 9 9 equal? c) Does 121= 11 11? c) Does 81= 9 9? 10
12 Simplifying Radicals Example 1: Simplify 20 Example 2: Simplify 28? 11
13 Practice Questions Directions: Simplify each square root as much as possible. 8= 18= 44= 32= 75= 50= 54= 108= 169= 128= 250= 200= 12
14 Jump Start 13
15 Exponent Tic-Tac Tac-Toe Toe 14
16 Practice Questions Directions: Simplify each of the square roots in Problems 1 5 as much as possible. 1) 98 2) 54 3) 144 4) 512 5) 756 6) What is the length of the unknown side of the right triangle? Simplify your answer in radical form. 15
17 7) What is the length of the unknown side of the right triangle? Simplify your answer in radical form. 8) What is the length of the unknown side of the right triangle? Simplify your answer in radical form. 9) Josue simplified 450 as Is he correct? Explain why or why not. 10) Tiah was absent from school the day that you learned how to simplify a square root. Using 360, write Tiah an explanation for simplifying square roots. 16
18 Thursday Exit Ticket Name: Directions: Simplify the square roots as much as possible and then complete the reflection. This is to be done independently and handed in for a grade by the end of class. If you finish early, study for your quiz tomorrow by looking over your Week 33 Packet. 1) 24 2) 338 3) 196 Reflection: On our scale of 0-5, rank how well you understand simplifying radicals and explain why. I would give myself a because 17
19 Week 32 Homework Directions: Determine the positive square root of the number given. If the number is not a perfect square, determine what square root it would be closest to. 1) 169 2) 256 3) 81 4) 147 5) 8 6) Which of the numbers in Problems 1 5 are rational numbers? Explain. 7) What positive value of makes the following equation true: =289? Explain. 18
20 8) A square shaped park has an area of 400 ft 2. What are the dimensions of the park? Write and solve an equation. 9) A cube has a volume of 64 in 3. What is the measure of one of its sides? Write and solve an equation. 10) What positive value of makes the following equation true: 125=? Explain. 19
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