1. **State the problem:** Solve for $\zeta$ in the equation $2\zeta = \frac{B}{m} \times \sqrt{\frac{m}{k}}$. 2. **Identify the formula and rules:** The equation relates $\zeta$ to constants $B$, $m$, and $k$. To isolate $\zeta$, we need to divide both sides by 2. 3. **Isolate $\zeta$:** $$ 2\zeta = \frac{B}{m} \times \sqrt{\frac{m}{k}} $$ Divide both sides by 2: $$ \zeta = \frac{1}{2} \times \frac{B}{m} \times \sqrt{\frac{m}{k}} $$ 4. **Simplify the expression:** Since $\sqrt{\frac{m}{k}} = \frac{\sqrt{m}}{\sqrt{k}}$, substitute: $$ \zeta = \frac{1}{2} \times \frac{B}{m} \times \frac{\sqrt{m}}{\sqrt{k}} = \frac{B}{2m} \times \frac{\sqrt{m}}{\sqrt{k}} $$ 5. **Combine terms:** $$ \zeta = \frac{B \sqrt{m}}{2 m \sqrt{k}} = \frac{B}{2 \sqrt{m} \sqrt{k}} $$ Because $\frac{\sqrt{m}}{m} = \frac{1}{\sqrt{m}}$. 6. **Final answer:** $$ \boxed{\zeta = \frac{B}{2 \sqrt{m k}}} $$ This is the expression for $\zeta$ in terms of $B$, $m$, and $k$.