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 $a=64.$