The approximate value of sqrt{63} is | vedclass

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Question

(A) We know that $\sqrt{64} = 8$.Since $63$ is very close to $64$, we can use the linear approximation formula: $f(x + \Delta x) \approx f(x) + f'(x)

Vedclass · Accepted Answer

$7.9373$

Vedclass · Answer

(A) We know that $\sqrt{64} = 8$.Since $63$ is very close to $64$, we can use the linear approximation formula: $f(x + \Delta x) \approx f(x) + f'(x) \Delta x$.Let $f(x) = \sqrt{x}$, $x = 64$, and $\Delta x = -1$.Then $f'(x) = \frac{1}{2\sqrt{x}}$.Substituting the values: $\sqrt{63} \approx \sqrt{64} + \frac{1}{2\sqrt{64}} (-1)$.$\sqrt{63} \approx 8 - \frac{1}{2 	imes 8} = 8 - \frac{1}{16}$.$\sqrt{63} \approx 8 - 0.0625 = 7.9375$.The closest value among the options is $7.9373$.

The approximate value of $\sqrt{63}$ is

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