Strontium has a larger atomic radius because it has more shells of electrons than magnesium does.
Mg is in Period 3 and Sr is in Period 5. Thus, Sr has two more shells of electrons than Mg.
Each shell is bigger than the one before it, so Sr has a larger atomic radius than Mg.
Both Sr and Mg have the same number of valence electrons, so they are not a factor in determining the atomic radius.
The nucleus is so small compared to the size of an electron shell that its size is not a factor in determining the atomic radius.