sqrt{1000000.000001} = ? | vedclass

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Question

(A) We need to find the square root of $1000000.000001$.Let $x = 1000000$ and $\Delta x = 0.000001$.We can use the binomial approximation $\sqrt{x + \

Vedclass · Accepted Answer

$1000$

Vedclass · Answer

(A) We need to find the square root of $1000000.000001$.Let $x = 1000000$ and $\Delta x = 0.000001$.We can use the binomial approximation $\sqrt{x + \Delta x} \approx \sqrt{x} + \frac{\Delta x}{2\sqrt{x}}$.Here,$\sqrt{x} = \sqrt{1000000} = 1000$.So,$\sqrt{1000000.000001} \approx 1000 + \frac{0.000001}{2 	imes 1000}$.$\sqrt{1000000.000001} \approx 1000 + \frac{0.000001}{2000} = 1000 + 0.0000000005 = 1000.0000005$.Since $1000.0000005$ is extremely close to $1000$,the most appropriate choice among the given options is $1000$.

$\sqrt{1000000.000001} = ?$

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