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Math 10C Unit 3—Roots and Powers Outcome Name:_________________ _ Definition Demonstrate an understanding of factors of whole numbers by determining the: prime factors greatest common factor least common multiple square root cube root. N1 Demonstrate an understanding of irrational numbers by: N2 N3 • representing, identifying and simplifying irrational numbers • ordering irrational numbers. Demonstrate an understanding of powers with integral and rational exponents. Vocabulary Composite number Factor tree Greatest common factor (GCF) Lowest common multiple (LCM) Prime Factorization Prime factors Cube Root Perfect cube Perfect Square Square Root Irrational and Rational Numbers Entire Radical Index Mixed radical Radicand Root Base Exponent Power Reciprocal Rational Exponents WS #1: Prime Factorization 1. Tell whether each number is prime, composite, or neither. 1 _________________ 29__________________ 45 _________________ 56__________________ 87 _________________ 93__________________ 15 _________________ 44__________________ 53 _________________ 31__________________ 110 ________________ 114_________________ 2. Find the prime factorization of each number. a) 42 e) 24 I) 120 b) 17 f) 97 j) 38 c) 102 g) 65 k) 40 d) 81 h) 18 l) 48 3. Find the LCM of the numbers by listing multiples. a) 3, 4 d) 5, 14 b) 8, 9 e) 8,9, 24 c) 15, 20 f) 12,9 4. Find the LCM of the numbers using prime factorization a) 30, 10 e) 30, 50 b) 42, 126 f) 75, 105 c) 54, 210 g) 8, 30, 45 d) 36, 54 h) 30, 70,105 5. Find the GCF of the following numbers using prime factorization a) 18, 20 6. 150, 225 b) 12, 27 e) 36, 54 c) 36, 60, 135 f) 30, 36, 75 d) 45, 75 g) 50, 56, 105 6. Samantha has two pieces of cloth. One piece is 72 inches wide and the other is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? 7. Ben exercises every 3 days and Isabel every 2 days. Ben and Isabel both exercised today. How many days in the next 30 days will they both exercise on the same day? 8. Use the Prime Factorization method to decide if these numbers are perfect squares and to find the square roots of those that are perfect squares. a) 225 d) 484 b) 400 f) 396 c) 360 g) 280 9. A cube has a volume of 512 cm3. Determine the surface area of the cube using prime factorization. WS # 2: Radicals 1. Determine what category the following numbers fall in. Natural, whole, integer, rational, irrational. Number 5 Category/ categories 4 3 125 5 8.25 90 2. Use the following radical to answer the next three questions. 5 100 a) What is the index? b) What is the radicand? c) What is the value of the radical, rounded to the nearest thousandth if appropriate? 3. Write each of the following as an entire radical. a) 3 2 d) 5 27 b) 4 3 e) 2 227 c) 2 5 f) 6 8 4. Write each of the following as an entire radical. a) 4 3 2 d) 5 3 2 b) 7 3 12 e) 14 3 12 c) 2 3 2 5. Write each of the following as a mixed radical. a) g) -1 125 5 32 b) - 27 c) 2 50 d) 1 2 e) -3 2 32 24 f) -3 98 3 h) i) 3 16 40 j) 5 3 24 k) 7 3 375 6. Order these numbers from greatest to least: , , , , 7. The speed, s, in meters per second, of an aircraft is related to the lift, L, in Newton’s, by the radical equation s = 0.1 L . When the lift is 1 440 000 N, then the speed, to the nearest meter per second, is _________m/s. WS # 3: Negative Exponents 1. Evaluate the following without using a calculator. a. ( 2) 3 b. 32 c. (6) 0 e. 31 7 g. 4 2 d. 8 1 f. 32 h. 52 2. Simplify a. y 14 y 6 4 x 2 2 c. 2x b. 58 52 d) ( x 3 y 5 )( x 4 y 3 ) 3. For each of the following solutions, identify the error that was made. Be specific about what the error is and determine the correct answer. a. ( ) 4x 3 2 = 4x 3´2 = 4x 6 æ a-2 ö-2 æ 4b3 ö2 ÷÷ = çç ÷÷ b. çç è 4b3 ø è a2 ø 2 3´2 =4 b a2´2 = 16b a4 6 WS #4: Rational Exponents 1. Write each expression in radical form. 1 4 3 a) 7 2 d) 7 3 h) (10m) 2 b) 3 44 3 62 c) 5 23 e) i) -1 (5n) 2 1 f) 2 6 6 j) (a) 5 g) (5x) -5 4 2. Write each expression in exponential form. a) ( 10 ) b) ( ) c) 4 5 2 ( 2) 3 3. Simplify a. 1 2 9 -4 b) 343 3 3 c) 36 2 3 d) ( 2) g) e) ( ) h) f) 6 4 5 5 ( 10 ) 6 ( m) 4 3 1 ( ) 3k 5 4. For the following solution, identify the error that was made. Be specific about what the error is and determine the correct answer. 5 8 4 = 8 54 -2 82 5-8 4 = 84 - 34 =8 4 3 =8 = ( ) 3 8 () = 2 = 16 4 4