Mathematico | Mathematico

You are given that

\sqrt{2} = 1.414 (4 s.f.)

By considering the change of sign of a suitable function, find the value of $\sqrt{2}$ to $5$ significant figures.

Consider

f (x) = x^{2} - 2

To save time, you can use the table mode in your calculator, using a starting value of $1.4135$ , an end value of $1.4145$ , and a step size of $0.0001$ .

Give the value of $\sqrt{2}$ to $5$ significant figures.