# Is 6 74 a real number

## Understand math 4, workbook

There is no real number whose square is a negative number. 11 a) 4 b) 4 c) ‒5 d) 21 e) 1 f) 1 12 2 13 a) 4 b) 9 c) 7 d) 11 e) 12 f) 20 14 a) 2 b) 3 c) 5 d) 10 e) 9 f) 12 15 16 a) 2 9 __ 2 d) 3 9 __ nb) 3 9 _ 7 e) 3a 9 ___ 2b c) 5 9 __ 11 f) 6 c 2 d 3 9 _ 7 17 Since 3888 = 4 · 972, the root is extracted from the factor 4, so 9 __ 4 = 2 comes before the root. Since 972 = 4 · 243, the root is taken from the factor 4, so another 9 __ 4 = 2 comes in front of the root. Since 243 = 9 · 27, the root is taken from the factor 9, so 9 __ 9 = 3 comes in addition to the root. Since 27 = 9 · 3, the root is taken from the factor 9, so 9 __ 9 = 3 comes in addition to the root. 18 a) d = 9 __ 20 b) d = 9 __ 45 c) d = 9 __ 29 d) d = 9 __ 13 19 0 1 2 3 4 5 6 √13 √13 20 0 1 2 3 4 5 7 8 6 2√10 √40 = 2√10 21 3 9 __ 3 ≈ 5.2 The hypotenuse length is 6 cm, the vertical cathetus length is 3 cm, ie. the horizontal cathetus length is 9 _____ 6 2 - 3 2 cm = 9 __ 27 cm = 3 9 __ 3 cm ≈ 5.2 cm. 22 a) 327m 2 21m ≈ 15.6m In this situation, a more precise rounding than to a decimeter is not advisable. b) 194 km3 ≈ 65 km In this situation, a more precise rounding than to kilometers is not advisable. c) 2m7 ≈ 0.286m In this situation, rounding to the nearest millimeter is necessary. d) (0.14mm + 0.021mm) 2 ≈ 0.08mm In this situation (average of two mean values) a more precise rounding than to two decimal places is not advisable. 23 If a number is irrational, it has to be rounded if you want to give it in decimal notation. If a number is rational, it cannot have any decimal places or can be rounded if you want to specify it in decimal notation; however, it can also have a period and can therefore be written in fractions. Solutions: 1 Real numbers 1 For testing purposes only - property of the publisher öbv