Question

How do you find the cube roots `root3(729)`?

Answer 1

`root(3)729=9`

Explanation:

Let us first factorize `729` in to rime factors. As sum of digits of `729` is `18`, it is divisible by `9` i.e. we can divide it twice by `3`. Therefore

`729=3xx3xx81`

Again `81` is `9^2`, hence divisible bt `3` four times more. Hence,

`729=3xx3xx3xx3xx3xx3xx3`

and `root(3)729=root(3)(ul(3xx3xx3)xxul(3xx3xx3))`

= `3xx3=9`