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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.
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).