Explanation

(b)
${(7.995)}^{\frac{1}{3}} = {(8 - 0.005)}^{\frac{1}{3}}$
$= {(8)}^{\frac{1}{3}}\left\lbrack 1 - \frac{0.005}{8} \right\rbrack^{\frac{1}{3}}$
$= 2\left\lbrack 1 - \frac{1}{3} \times \frac{0.005}{8} + \frac{\frac{1}{3}\left( \frac{1}{3} - 1 \right)}{2 \bullet 1}\left( \frac{0.005}{8} \right)^{2} + ... \right\rbrack$
$= 2\left\lbrack 1 - \frac{0.005}{24} - \frac{\frac{1}{3} \times \frac{1}{3}}{1} \times \frac{(0.005)^{2}}{64} + ... \right\rbrack$
$= 2(1 - 0.000208)$ (neglecting other terms)
$= 2 \times 0.999792$
$= 1.9996$