Question

Find the approximate value of \(\sqrt{11}\).

(a) 3.34

(b) 3.934

(c) 3.0034

(d) 3.544

I got this question in a job interview.

The question is from Derivatives Application in division Application of Derivatives of Mathematics – Class 12

Answer 1

Right answer is (a) 3.34

The best I can explain: Let y=\(\sqrt{x}\). Let x=9 and Δx=2

Then, Δy=\(\sqrt{x+Δx}-\sqrt{x}\)

 Δy=\(\sqrt{11}-\sqrt{9}\)

\(\sqrt{11}\)=Δy+3

dy is approximately equal to Δy is equal to

dy=\(\frac{dy}{dx}\)Δx

dy=\(\frac{1}{(2\sqrt{x})}\).Δx

dy=\(\frac{1}{(2\sqrt{9})}(2)\)

dy=2/6=0.34

∴ The approximate value of \(\sqrt{11}\) is 3+0.34=3.34.