Question 263·Easy·Advanced Math

The equation has $m$ multiplying $n^2$. Divide both sides by $m$; the problem says $m$ is positive, so it cannot be zero:

For a sample check, type $m=2$, $k=4$, and $mn_{1}^{2}\sim8k\left\{n_{1}>0\right\}$. The $\sim$ tells Desmos to find a value that fits the equation, and the braces restrict it to positive values. Under PARAMETERS, Desmos reports $n_{1}=4$. That's one valid case, not a formula for every $m$ and $k$.

Dividing by $m$ isolated $n^2$, not $n$. Take the square root of both sides to undo the square. A negative number could have the same square, but $n$ must be positive, so use the positive square root:

That expresses $n$ in terms of $m$ and $k$. Choice C.