Question

Using the binomial expansion upto $3$ terms the approximate value of $(8.8{)}^{1/3}$ can be shown to be

• A. $2+\frac{67}{900}$
• B. $2+\frac{107}{900}$
• C. $2+\frac{58}{900}$
• D. $2+\frac{47}{900}$

Answer 1

The correct option is C $2+\frac{58}{900}$

The value of $(8.8{)}^{1/3}$
$=8^{1/3}{1.1}^{1/3}$
$=2(1.1{)}^{1/3}$
$=2(1+0.1{)}^{1/3}$
$=2(1+\frac{0.1}{3}+\frac{-2}{9.2!}(0.1{)}^2...\infty )$
$=2(1+\frac{1}{30}-\frac{1}{900}...\infty )$
$=2+\frac{\left(2\right)30}{900}-\frac{2}{900}...\infty$
$=2+\frac{60}{900}-\frac{2}{900}...\infty$
$=2+\frac{58}{900}...\infty$
Hence, the value of $(8.8{)}^{1/3}$ correct upto $3$ decimal places is
$2+\frac{58}{900}$