A simple way of approximating 30 3 {\displaystyle {\sqrt[{3}]{30}}} is to construct the linear approximation of (i.e., tangent line to) f ( x ) = x 3 {\displaystyle f(x)={\sqrt[{3}]{x}}} at some point ( a , f ( a ) ) {\displaystyle (a,f(a))} for which f ( a ) {\displaystyle f(a)} is known exactly and a ≈ 30. {\displaystyle a\approx 30.}
![{\displaystyle {\sqrt[{3}]{30}}}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/fadbc0786cf1014cf601370f05d9eb5270a0a179)
![{\displaystyle f(x)={\sqrt[{3}]{x}}}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/7b1d312e15e009bd6c705519b2b1b7400cf1c368)
