Annual volatility = sqroot(Time periods) x daily volatility

When calculating annual variance we multiply by 251 (time periods). So when translating this into the annual std dev, we also have to sqrRoot time periods right? i.e this is the reason for squaring root the time periods no?

the reason is that we are square rooting the variance to get to stdev. So any scaling to get to other period stdev needs to be done my multiplying or dividing by the square root of time period segments.

Given this formula:

Annual volatility = sqroot(Time periods) x daily volatility

When calculating annual variance we multiply by 251 (time periods). So when translating this into the annual std dev, we also have to sqrRoot time periods right? i.e this is the reason for squaring root the time periods no?

the reason is that we are square rooting the variance to get to stdev. So any scaling to get to other period stdev needs to be done my multiplying or dividing by the square root of time period segments.

If we want to compare implied vol and historical vol, for historical vol: do we take sample std or population std (i.e divide by n or n-1)?

N-1 same stdev