Using differentials, find the approximate value of `(0. 009)^(1//3)`

Explanation

We have to find the approximate value of
`(0. 009)^(1/3)`
consider `y=x^(1/3)`
Let `x=0.008` and `Δx=0.001`.

Then,

`Δy=(x+Δx)^(1/3)-x^(1/3)`
`=(0.009)^(1/3)-0.2`
`=>(0.009)^(1/3)=0.2+Delta y`
Now, dy is approximately equal to `Δy `and is given by,

`dy=((dy)/(dx))Delta x=1/(3(x)^(2/3))(Delta x)`
`=1/(3(0.04))(0.001)`
`=0.001/0.12`
`0.008`
Hence, the approximate value of `(0.009)^(1/3)` is
`0.2+(0.008)`
`=0.208`