A) 1.9995
B) 1.9996
C) 1.9990
D) 1.9991
Correct Answer: A
Solution :
\[{{(7.995)}^{1/3}}={{(8-0.005)}^{1/3}}={{(8)}^{1/3}}\] \[{{\left[ 1-\frac{0.005}{8} \right]}^{1/3}}\] \[=2\,\,\left[ 1-\frac{1}{3}\times \frac{0.005}{8}+\frac{\frac{1}{3}\left( \frac{1}{3}-1 \right)}{2+1}{{\left( \frac{0.005}{8} \right)}^{2}}+..... \right]\] \[=2\,\left[ 1-\frac{0.005}{24}-\frac{\frac{1}{3}\times \frac{1}{3}}{1}\times {{\frac{(0.005)}{8}}^{2}}+..... \right]\] \[=2(1-0.000208)=2\times 0.999792=1.9995\]
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