# Is 3 27 a rational number

## This is math 4, workbook

3 solutions 41 a) √ ___ 4 2 = 2 √ _ 2 d) √ ___ 9 5 = 3 √ _ 5 g) √ ____ 49 2 = 7 √ _ 2 b) √ ___ 9 3 = 3 √ _ 3 e) √ ____ 25 2 = 5 √ _ 2 h) √ ____ 36 3 = 6 √ _ 3 c) √ ____ 16 2 = 4 √ _ 2 f) √ ____ 36 2 = 6 √ _ 2 42 a) y √ _ 5 c ) a 2 √ __ 10 e) 2 a √ _ 2 g) 5 ab √ _ 2 b) z √ _ 3 d) 5 √ __ b f) 6b √ __ a h) 4 a √ ___ 2b 2 cube root (page 12) 43 a) 3 √ __ 64 = 4 because 4 3 = 64. b) 3 √ ____ 8,000 = 20, because 20 3 = 8,000. 44 a) 2 <3 √ ___ 20 <3, because 2 3 = 8, 3 3 = 27 b) 4 <3 √ ___ 100 <5, because 4 3 = 64, 5 3 = 125 c) 5 <3 √ ___ 200 <6, because 5 3 = 125, 6 3 = 216 d) 7 <3 √ ___ 400 <8, because 7 3 = 343, 8 3 = 512 45 a) 3 √ _ 8 = 2 b) 3 √ ___ 125 = 5 c) 3 √ __ 64 = 4 d) 3 √ ___ 2.7 ≈ 1.39 3 √ ___ 0.8 ≈ 0.93 3 √ ___ 12.5 ≈ 2.32 3 √ ___ 640 ≈ 8.62 3 √ ___ 0.27 ≈ 0.65 3 √ ___ 0.08 ≈ 0.43 3 √ ___ 1.25 ≈ 1.08 3 √ ____ 6400 ≈ 18.57 3 √ ____ 0.027 = 0.3 3 √ ____ 0.008 = 0.2 3 √ ____ 0.125 = 0.5 3 √ _____ 64 000 = 40 3 √ _____ 0.0027 ≈ 0.14 Finite decimal numbers are obtained with 1000 times or one thousandth of cube numbers. 46 1) D 2) calculated: V = m __ ρ = 153.6 ___ 300 m 3 = 0.512m 3 = 512dm 3 ➞ s = 3 √ ___ 512 dm = 8dm 3 real numbers and number ranges ( Pages 12, 13) 47 C 48 a) QNRZI b) In contrast to irrational numbers, rational numbers can be written in fractions. Rational numbers are decimal numbers with a finite number of digits or periodic decimal numbers; Irrational numbers are decimal numbers with an infinite number of digits without a period. 49 Number ℕ ℤ ℚ ℝ I 3 √ __ 64 2.5 · 10 5 π 13 0.143143… 1.010010001… - 2.5 · 10 1 √ __ 27 20% 50 correct: A, C, D, F, H, I, L, M, N; wrong: B, E, G, J, K, O, P, Q, R Solution text: IM * PRATER * BLUEHEN * AGAIN * THE * TREES! 4 intervals (page 14) 51 a) [- 4; 2) -4 -3 -2 -1 0 1 2 3 b) (- 1; 4) -2 -1 0 1 2 3 4 5 c) [- 3; 3] -3 -2 -1 0 1 2 3 4 52 a) [- 10; 10], - 10 ≤ x ≤ 10 b) (- 3; 5], - 3

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