By making use of the relation \(\delta y \approx \dfrac{dy}{dx} \times \delta x\), and without using tables, prove that \(5.1\) is an approximate value of \(\sqrt{26}\).

By making use of the relation \(\delta y \approx \dfrac{dy}{dx} \times \delta x\), and without using tables, prove that \(5.1\) is an approximate value of \(\sqrt{26}\).