Question

Find the approximate value of \(\sqrt{49.1}\).

(a) 7.0142

(b) 7.087942

(c) 7.022

(d) 7.00714

I had been asked this question during an interview.

My question is based upon Derivatives Application topic in division Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (d) 7.00714

Easiest explanation: Let y=\(\sqrt{49.1}\). Let x=49 and Δx=0.1

Then, Δy=\(\sqrt{x+Δx}-\sqrt{x}\)

 Δy=\(\sqrt{49.1}-\sqrt{49}\)

\(\sqrt{49.1}\)=Δy+7

dy is approximately equal to Δy is equal to

dy=\(\frac{dy}{dx}\)Δx

dy=\(\frac{1}{(2\sqrt{x})}\).Δx

dy=\(\frac{1}{(2\sqrt{49})}\) (0.1)

dy=0.1/14=0.00714

∴ The approximate value of \(\sqrt{49.1}\) is 7+0.00714=7.00714