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Errors in algebra
Published in Breach Mark, Essential Maths for Engineering and Construction, 2017
There is no real value for the square root of a negative number. The square root of a negative number can be expressed in complex form as the product of the square root of a positive number and i, the square root of −1. For example, -7=7i, where i=-1.
Mathematics for Engineering Technicians
Published in Mike Tooley, BTEC First Engineering, 2010
The square root of a number is when the index is ½. The square root of 2 is written as 2½ or √2. The value of a square root is the value of the base which when multiplied by itself gives the number. Since 3 × 3 = 9, then √9 = 3. However, (−3) × (−3) = 9, so we have a second possibility, i.e. √9 = ±3. There are always two answers when finding the square root of a number and we can indicate this is by placing a ± sign in front of the result meaning ‘plus or minus’. Thus: 4½=√4=±2 and 9½=√9=±3.Another viewAppendix 2 provides you with a detailed introduction to the Casio fx-83ES calculator. If you are unfamiliar with using a scientific calculator you should work through the examples given in the Appendix before using your calculator to solve the Test your knowledge problems that follow.
Electrical science and principles
Published in Trevor Linsley, Electrical Installation Work Level 2, 2019
The three-phase windings of an a.c. generator may be star connected or delta connected as shown in Fig. 2.79. The important relationship between phase and line currents and voltages is also shown. The square root of 3 (√3) is simply a constant for three-phase circuits, and has a value of 1.732. The delta connection is used for electrical power transmission because only three conductors are required. Delta connection is also used to connect the windings of most three-phase motors because the phase windings are perfectly balanced and, therefore, do not require a neutral connection.
Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery
Published in Journal of Asian Architecture and Building Engineering, 2019
This paper provides an in-depth discussion of the square root of 25The square root of 2 is an irrational number. It cannot strictly be measured with a ruler based on our unit of measurement, no matter how small we mark fractional subdivisions. However, when we calculate the length of the diagonal of a rectangle, employing the Pythagorean Theorem, we obtain, indirectly, an irrational number (Carnap 1995)., using mathematics and astronomical books, such as the Jiuzhang Suanshu (The Nine Chapters on the Mathematical Art) and the Zhoubi Suanjing (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven), which was written by an anonymous author around the 1st century BC. Korea’s ancient history book, the Samguk sagi (History of the Three Kingdoms), mentions in the chapter seven of the Silla government offices in Book 38 that the Jiuzhang Suanshu was used in the 7th-8th centuries as a regular mathematics textbook in the Sanhak department 算學科 (arithmetic education) at the Silla-era Kukhak 國學 (the state-run educational institution). It is possible that the Jiuzhang Suanshu entered the peninsula at this time. The Nine Chapters of the Jiuzhang Suanshu examine Gougu 勾股 (base and altitude), in close association with the Zhoubi Suanjing. Liu Hui comments on the first three problems of the chapter, which use the case of base 3, altitude 4 and hypotenuse 5 to illustrate how each side may be found using the other two. Specifically, Liu explores instructions for finding the square root of the hypotenuse from the sum of the squares of the other two sides (Cullen 2007, 88).
Exploration of a Fast Pathway to Nuclear Fusion: Thermal Analysis and Cooling Design Considerations for the ARC Reactor
Published in Fusion Science and Technology, 2020
S. Segantin, R. Testoni, Z. Hartwig, D. Whyte, M. Zucchetti
The coolant temperatures are relatively high in the whole power range; namely, the difference between the two values of Tout for the different powers is quite small compared to the difference of any Tout to Tamb. In addition to this, the temperature ratio in Eq. (3) is under the square root. These aspects give the efficiency an almost flat behavior in the tokamak’s power range, which appears ideal for a load-following power plant.
Prospective mathematics teachers learning complex numbers using technology
Published in International Journal of Mathematical Education in Science and Technology, 2022
Jorge Gaona, Silvia Soledad López, Elizabeth Montoya-Delgadillo
To represent the square root of a negative number other than , the form bi is used, where b is any real number and i is the imaginary unit (called a pure imaginary number).