As the square root is a monotonic function on the positive domain, taking the square root would have no effect on any model selection. Could you please mention a use-case when it taking the root has some real advantage?

As the square root is a monotonic function on the positive domain, taking the square root would have no effect on any model selection

This is why we reject it previously I think (though I'm unable to find relevant discussions)
I'd argue that given the popularity of RMSE, it might be worthwhile to add several lines of (redundant) code for it (we only need <5 lines of code for the metric I think)
Sometimes users might want to report the RMSE of their model instead of MSE, because RMSE is more meaningful (i.e., it reflects the deviation between actual value and predicted value).

Hi,
If there is a consensus on this I would like to give this a try.

If there is a consensus on this I would like to give this a try.

not yet, please wait or try another issue.

Hmm, I found #6457 (comment)

I would like to work on this.

Is this still open? I would like to work on it.

you can start your work based on the stalled PR.

I think we should indeed add this.

@amueller @qinhanmin2014 Could you please review the PR, which I created. PR #13467

Mean Squared Error ( MSE ) is defined as Mean or Average of the square of the difference between actual and estimated values. This means that MSE is calculated by the square of the difference between the predicted and actual target variables, divided by the number of data points. It is always non–negative values and close to zero are better.

Root Mean Squared Error is the square root of Mean Squared Error (MSE). This is the same as Mean Squared Error (MSE) but the root of the value is considered while determining the accuracy of the model.