Science:Math Exam Resources/Courses/MATH104/December 2016/Question 04 (a)/Hint 1

A simple way of approximating ${\sqrt {69}}$ is to construct the linear approximation of (i.e., tangent line to) $f(x)={\sqrt {x}}$ at some point $(a,f(a))$ for which $f(a)$ is known exactly. Therefore, the point needs to satisfy two things: have a pretty straightforward square root and also close to ${\sqrt {69}}$. Thus we choose $a=64.$