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 \(\sqrt{26}\).

There is a convention in maths that \(\delta y\) signifies ‘a small increase in \(y\)’.

We need to specify \(y=f(x)\). Can we think of an appropriate \(f(x)\), given that we’re trying to find \(\sqrt{26}\)?

What happens if we choose \(y = \sqrt{x}\)?

If we take \(y = \sqrt{x}\), what happens if we then use \(x = 25\) and \(\delta x = 1\)?