Q57 / 120 · VITEEE 2011 · Mathematics

Find the value of $(7.995)^{1 / 3}$ correct to four decimal places.

A
$1.9995$
Correct answer
B
$1.9996$
C
$1.9990$
D
$1.9991$

Solution

$$ \begin{array}{l} (7.995)^{1 / 3}=(8-0.005)^{1 / 3} \\ =2\left(1-\frac{0.005}{8}\right)^{1 / 3} \\ =2\left[1+\left(\frac{1}{3}\right)\left(-\frac{0.005}{8}\right)\right]=2[1-0.000208] \\ =1.9996 \end{array} $$

Hence, the correct answer is option: 'B'.

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