The approxiamte value of `(0.007)^(1/3)` is

Options

A. `21/120`
B. `23/120`
C. `29/120`
D. `31/120`

Answer

B

Explanation

Let `f(x)=x^(1//3)`
Now `f(x+Deltax)-f(x)=f'(x).Deltax=(Deltax)/(3x^(2//3))`
We may write `0.007=0.008-0.001`
Taking `x=0.008` and `Deltax=-0.001`
We get `f(0.007)-f(0.008)~=-0.001/(3(0.008)^(2//3))`
or `f(0.007)-f(0.008)~=1/120`
`:.f(0.007)~=f(0.008)-1/120=0.2-1/120`
`implies (0.007)^(1//3)~=23/120`