How can I get nth root of real numbers

[Chen Samulsion]

Dear Stata users,

In Stata there's a function sqrt() to get the square root of x. Now I want to caculate the nth root of x, and is there any function to achieve this? Thank you.

[Joseph Coveney]

Are you looking for something like this?

di exp(ln(16)/3)
di 16^(1/3)

Or are you looking for something like Mata's polyroots()?

[Joseph Coveney]

Keep in mind that if the former, then you'll need to separately keep track of the argument's sign.

[Chen Samulsion]

Joseph Coveney, thank you very much! That is exactly what I want.

[Nick Cox]

Odd integer roots are sometimes of interest and they are defined for negative arguments too. Cube roots are in my reading by far the most common example. Thus just as -8 is the cube of -2, so by the same principle -2 is the cube root of -8. But to get cube roots correctly in Stata you need something more like

sign(x) * (abs(x))^(1/3)

The reason is that powering is usually implemented in terms of logarithms, for which arguments must be positive. (It is easy enough to trap zero arguments.)

[Chen Samulsion]

Nick Cox, thank you very much. And congratulate on your 34567 posts.

[Nick Cox]

Ha! I like that. It is not prime as it is the product 13 x 2659.