Solve T=fsqrt{M/n}

$$T = f \sqrt { \frac { M } { n } }$$

Solve for M

$$\left\{\begin{matrix}M=\left(\frac{T}{f}\right)^{2}n\text{, }&\left(f<0\text{ or }T\geq 0\right)\text{ and }\left(f>0\text{ or }T\leq 0\right)\text{ and }f\neq 0\text{ and }n\neq 0\\M\geq 0\text{, }&T=0\text{ and }f=0\text{ and }n>0\\M\leq 0\text{, }&T=0\text{ and }f=0\text{ and }n<0\\M=0\text{, }&n\neq 0\text{ and }T=0\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$f\sqrt{\frac{M}{n}}=T$$

Divide both sides by f.

$$\frac{f\sqrt{\frac{1}{n}M}}{f}=\frac{T}{f}$$

Dividing by f undoes the multiplication by f.

$$\sqrt{\frac{1}{n}M}=\frac{T}{f}$$

Square both sides of the equation.

$$\frac{1}{n}M=\frac{T^{2}}{f^{2}}$$

Divide both sides by n^{-1}.

$$\frac{\frac{1}{n}Mn}{1}=\frac{T^{2}}{f^{2}\times \frac{1}{n}}$$

Dividing by n^{-1} undoes the multiplication by n^{-1}.

$$M=\frac{T^{2}}{f^{2}\times \frac{1}{n}}$$

Divide \frac{T^{2}}{f^{2}} by n^{-1}.

$$M=\frac{nT^{2}}{f^{2}}$$

Solve for M (complex solution)

$$\left\{\begin{matrix}M=\left(\frac{T}{f}\right)^{2}n\text{, }&f\neq 0\text{ and }\left(T=0\text{ or }|arg(\sqrt{\frac{T^{2}}{f^{2}}}f)-arg(T)|<\pi \right)\text{ and }n\neq 0\\M\in \mathrm{C}\text{, }&T=0\text{ and }f=0\text{ and }n\neq 0\end{matrix}\right.$$

Solve for T (complex solution)

$$T=\sqrt{\frac{M}{n}}f$$

$$n\neq 0$$

Solve for T

$$T=\sqrt{\frac{M}{n}}f$$

$$\left(M\geq 0\text{ and }n>0\right)\text{ or }\left(M\leq 0\text{ and }n<0\right)$$