Question

Find the approximate value of \(\sqrt{64.3}\).

(a) 8.0675

(b) 8.03465

(c) 8.01875

(d) 8.0665

I have been asked this question during an online interview.

Asked question is from Derivatives Application topic in section Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (c) 8.01875

The explanation: Let y=\(\sqrt{x}\). Let x=64 and Δx=0.3

Then, Δy=\(\sqrt{x+Δx}-\sqrt{x}\)

Δy=\(\sqrt{64.3}-\sqrt{64}\)

\(\sqrt{64.3}\)=Δy+8

dy is approximately equal to Δy is equal to:

dy=\(\frac{dy}{dx}\)Δx

dy=\(\frac{1}{2\sqrt{x}}\).Δx

dy=\(\frac{1}{2\sqrt{64}}\) (0.3)

dy=0.3/16=0.01875

∴ The approximate value of \(\sqrt{64.3}\) is 8+0.01875=8.01875