= Solution
At fixed <temperature> and <solvent> <permittivity>, the <Debye–Hückel screening length> satisfies $\lambda_D^{-2}\propto\sum_i c_i z_i^2=2I$, where $I=\tfrac12\sum_i c_i z_i^2$ is <ionic strength>. Fully dissociated <sodium chloride> has two monovalent <ion> species, giving $I_1=0.01$ M. Fully dissociated <magnesium sulfate> has two divalent species, giving
$$
I_2=\tfrac12[0.1(2)^2+0.1(-2)^2]=0.40\,\mathrm M.
$$
The <multivalent-electrolyte screening-length ratio> is therefore
$$
\boxed{\lambda_{D,2}=3\,\mathrm{nm}\sqrt{\frac{0.01}{0.40}}=0.474\,\mathrm{nm}\simeq0.47\,\mathrm{nm}.}
$$
The squared valences are essential: counting only the total <ion> <concentration> misses a factor of four in the screening strength per formula unit. This is the comparable linear-screening estimate, assuming unchanged dielectric response and full dissociation. <ion pairs> and concentrated-electrolyte nonideality can make a real divalent-salt solution depart from it; no such correction is specified.
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