Question

If `root(3)(729)` = 9 then `root(3)(0.000729) = ?`

Answer 1

It is given that , 

`root(3)(729)` = 9

`root(3)(0.000729) = root(3)(729/1000000)`

= `root(3)(729)/root(3)(1000000)`

= `root(3)(9^3)/root(3)((100)^3)`

= `9/100`

= 0.09

Answer 2

The cube root of `729` is 9 because `9×9×9=729`. Now, we need to determine the cube root of `0.000729.`

To solve for `root(3){0.000729}​`, we can express the number in a form similar to 729:

`0.000729 = \frac{729}{10^6} = 729 \times 10^{-6}`

Using the property of cube roots:

`root(3)(729×10^{-6})=root(3)(729)×root(3)(10^{-6}`

Since `root(3)(729)=9 and root(3)(10^{-6})=10^{-2}`, we get:

`9×10^{-2}=9×0.01=0.09`

Thus, the cube root of 0.0007290 is:

`0.09​`