Two unknown 3d transition metal chlorides, Salt A and Salt B, are...

The reaction of metal cations with potassium ferrocyanide, $\mathrm{K}_4[\mathrm{Fe}(\mathrm{CN})_6]$, gives characteristic precipitates.

Salt A forms a chocolate brown precipitate, which indicates the presence of the $\mathrm{Cu}^{2+}$ ion. The precipitate is cupric ferrocyanide, $\mathrm{Cu}_2[\mathrm{Fe}(\mathrm{CN})_6]$.
The electronic configuration of $\mathrm{Cu}^{2+}$ is $[\mathrm{Ar}] 3d^9$. It has $1$ unpaired electron ($n = 1$).
Spin-only magnetic moment $\mu = \sqrt{n(n+2)} = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \text{ BM}$.

Salt B forms a Prussian blue precipitate, which indicates the presence of the $\mathrm{Fe}^{3+}$ ion. The precipitate is ferric ferrocyanide, $\mathrm{Fe}_4[\mathrm{Fe}(\mathrm{CN})_6]_3$.
The electronic configuration of $\mathrm{Fe}^{3+}$ is $[\mathrm{Ar}] 3d^5$. It has $5$ unpaired electrons ($n = 5$).
Spin-only magnetic moment $\mu = \sqrt{n(n+2)} = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ BM}$.

Therefore, the spin-only magnetic moments are $1.73$ and $5.92$ respectively.

Answer: $1.73$ and $5.92$