More Surd Approximations... | Linear Approximation

Exercise 8.1 - Question 2 (ii) and (iii) from "Mathematics XII - Volume I and II" by the Department of School Education under the Government of Tamil Nadu. Question 2 (ii): We are asked to find the approximate value of the 4th root of 15, i.e., (15)^{1/4}. We first identify the function involved in the question (which is the 4th root function defined on R ), then apply the definition of 'linear approximation' of the given function at 16, which is a perfect 4th-power number close to 15. This new function is L(x). Then, we use L(x) to find the required approximation by setting x = 15 in L(x). Question 2 (iii): We are asked to find the approximate value of the cube root of 26. We first identify the function involved in the question (which is the cube root function defined on R ), then apply the definition of 'linear approximation' of the given function at 27, which is a perfect cube close to 15. This new function is L(x). Then, we use L(x) to find the required approximation by setting x = 26 in L(x). CONTENT and PRESENTATION: Sasitharan E. CAMERA and EDITING: Edilebert R., SPSC Location: St. Peter's Study Centre (SPSC), Puducherry 605003.