If x be so small that its square and higher powers may be neglected, find the value of :
$\frac{(8 + 3 x)^{\frac{2}{3}}}{(2 + 3 x) \sqrt{4 - 5 r}}$

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Solution

$\Rightarrow {(8 + 3 x)}^{2 / 3} {(2 + 3 x)}^{- 1} {(4 - 5 x)}^{- 1 / 2}$
$\Rightarrow 4 (1 + \frac{2 x}{8}) \frac{1}{2} (1 - \frac{3 x}{2}) \frac{1}{2} (1 + \frac{5 x}{8})$
$\Rightarrow (1 + \frac{2 x}{8}) (1 - \frac{3 x}{2}) (1 + \frac{5 x}{8})$
$\Rightarrow (1 - \frac{5 x}{4}) (1 + \frac{5 x}{8})$
$\Rightarrow 1 - \frac{5 x}{4} + \frac{5 x}{8} = 1 - \frac{5 x}{8} . . .$

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