volatility - Square root of time

I am writing about VaR and I am wondering about the following: We can scale the VaR to different time horizons by using the square root of time, which means, that the volatility is adjusted by square root of the time horizon. So e.g. we have the daily volatility then the weekly volatility (for 5 trading days) is given by

$\sqrt{5}*$ daily volatility

Now my question is the following:

Does this hold only for log returns or also for simple returns?

I googled it but I could not find a proof for it. So where can I find a proof for this in terms of log returns and either also a proof for the case of simple returns or an estimation of the error I will be doing, if I use the square root of time while using simple returns?

And finally considering the VaR: Does this need the normal distribution as an assumption?