The approximate value of sqrt{6560} is | vedclass

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Question

(A) To find the approximate value of $\sqrt{6560}$,we can use the linear approximation formula: $\sqrt{x + \Delta x} \approx \sqrt{x} + \frac{\Delta x

Vedclass · Accepted Answer

$80.9939$

Vedclass · Answer

(A) To find the approximate value of $\sqrt{6560}$,we can use the linear approximation formula: $\sqrt{x + \Delta x} \approx \sqrt{x} + \frac{\Delta x}{2\sqrt{x}}$.We know that $81^2 = 6561$.Let $x = 6561$ and $\Delta x = -1$.Then,$\sqrt{6560} = \sqrt{6561 - 1} \approx \sqrt{6561} - \frac{1}{2\sqrt{6561}}$.$\sqrt{6560} \approx 81 - \frac{1}{2 	imes 81} = 81 - \frac{1}{162}$.$\frac{1}{162} \approx 0.0061728$.Therefore,$\sqrt{6560} \approx 81 - 0.0061728 = 80.9938272$.Rounding to four decimal places,we get $80.9938$. Comparing this with the given options,$80.9939$ is the closest approximation.

The approximate value of $\sqrt{6560}$ is

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