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Find the approximate value of √0.037 using differential approxmations? ​

Answer 1

Answer:

Hence, the approximate value of √0.037 is 0.1925.

Explanation:

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Answer 2

Answer:

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$Take \: \: y = \sqrt{x}$

$Let \: x = 0.04 \: and \: ∆ x = 0.03$

$Then \: ∆y = \sqrt{x + ∆x} - \sqrt{x}$

$∆y = \sqrt{0.037 - } \sqrt{0.04 }$

$\sqrt{0.037 = } ∆</p><p></p><p>y + 0.2$

Now, dy is approximately equal to $$Δy$$ and is given by

$dy = ( \frac{dy}{dx} )∆x$

$= \frac{1}{2 \sqrt{x} } (0.003)$

$= 2 \sqrt{0.004} (0.003)$

=0.0075

Thus the approximate value of √0.037 is 0.2-0.0075 = 0.1925

Hence, this is the answer