Just to expand, let's say the assumptions needed for the variances to be identical and additive are satisfied, so the annual variance will be the sum of monthly variances. I am going to assume 360 days in a year but you will have to change it to reflect the local holidays/weekends etc. So the annual variance will be the sum of 12 monthly variances:
$\sigma^2_{360d}=12 \times \sigma^2_{30d}$
$\sigma^2_{360d}=\sigma^2_{30d}\frac{360}{30}$
You can similarly write for the 2-days horizons:
$\sigma^2_{360d}=\sigma^2_{2d}\frac{360}{2}$
Hence,
$\sigma^2_{360d}=\sigma^2_{30d}\frac{360}{30}=\sigma^2_{2d}\frac{360}{2}$
And if you rearrange you get:
$\sigma^2_{2d}=\sigma^2_{30d}\frac{2}{30}$
The square root of which is the relationship you have, but this is the relationship between the volatility of return over 30 days and the volatility of returns over 2 days as @Ami44 explained above. If the assumptions for variances to be additive are satisfied then both shall give the same annual volatility when annualised.