Name ___________ 8- ____________ Exit Tickets 8M7_8M1 Date __________ Math Lesson 2: Square Roots 1. What is the value of √𝑥 2 . Answer __________________ 2. The area of a square piece of land is 225 sq feet. What is the side length of the land? Show work Answer _________________ 3. The positive square root of 50 is not an integer. Which whole number does the value of √50 lie closest to? Show work. Answer __________________________________________ Explain. Place the following numbers on the number line in approximately the correct positions: √16, √9, √11, and 3.5. 1 Lesson 3: Existence and Uniqueness of Square Roots and Cube Roots Find the positive value of 𝑥 that makes each equation true. Check your solution. 4. 𝑥 2 = 169 a. Explain the first step in solving this equation. b. Solve and check your solution. Answer____________________________________________ 5. 𝑥 3 = 216 Answer____________________________________________ 2 Lesson 1: Exponential Notation 1. a. Express the following in exponential notation: (−13) × ⋯ × (−13). ⏟ 35 times Answer___________________________________________ b. Will the product be positive or negative? Explain. 2. Fill in the blank: 2 2 2 4 × ⋯× = ( ) ⏟ 3 3 3 _______times Answer______________________ 2 4 What is another way to express ( ) using exponents? 3 Answer______________________ 3. Arnie wrote: (⏟−3.1) × ⋯ × (−3.1) = −3.14 4 times Is Arnie correct in his notation? Why or why not? 3 Lesson 2: Multiplication of Numbers in Exponential Form Write each expression using the fewest number of bases possible. 1. Let 𝑎 and 𝑏 be positive integers. 23𝑎 × 23𝑏 = Answer___________________________________________ 2. 53 × 25 = Answer___________________________________________ 3. Let 𝑥 and 𝑦 be positive integers. 11𝑥 11𝑦 = Answer___________________________________________ 4. 213 23 = Answer___________________________________________ 4 Lesson 3: Numbers in Exponential Form Raised to a Power Write each expression as a base raised to a power or as the product of bases raised to powers that is equivalent to the given expression. 1. (93 )6 = Answer___________________________________________ 2. Let 𝑥, 𝑦, 𝑧 be numbers. (𝑥 2 𝑦𝑧 4 )3 = Answer___________________________________________ 3. 48 58 = Answer___________________________________________ Lesson 4: Numbers Raised to the Zeroth Power 1. Simplify the following expression as much as possible. 410 0 ∙7 = 410 Answer__________________________ 5 Lesson 5: Negative Exponents and the Laws of Exponents Write each expression in a simpler form that is equivalent to the given expression. 1. 76543−4 = Answer__________________________ 2. Let 𝑓 be a nonzero number. 𝑓 −4 = Answer__________________________ 3. Let 𝑎, 𝑏 be numbers (𝑏 ≠ 0). 𝑎𝑏 −1 = Answer__________________________ 4. Let 𝑔 be a nonzero number. 1 𝑔−1 = Answer________________________ 6 Lesson 9: Scientific Notation 1. The approximate total surface area of Earth is 5.1 × 108 km2 . All the salt water on Earth has an approximate surface area of 352,000,000 km2 , and all the freshwater on Earth has an approximate surface area of 9 × 106 km2 . How much of Earth’s surface is covered by water, including both salt and fresh water? Write your answer in scientific notation. Total Surface Area_________________________ Salt Water Area____________________________ Fresh Water Area__________________________ Answer__________________________ 2. How much of Earth’s surface is covered by land? Write your answer in scientific notation. Answer__________________________ 3. Approximately how many times greater is the amount of Earth’s surface that is covered by water compared to the amount of Earth’s surface that is covered by land? Answer__________________________ 7 Lesson 10: Operations with Numbers in Scientific Notation 1. The speed of light is 3 × 108 meters per second. The sun is approximately 230,000,000,000 meters from Mars. How many seconds does it take for sunlight to reach Mars? Lesson 13: Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology 1. Compare 2.01 × 1015 and2.8 × 1013 . Which number is larger? How do you know? Answer___________________________________________ 2. Compare 6.5 × 10−9 and4.75 × 10−9 . Which number is larger? How do you know? Answer________________________________________ 8