Solve P=sqrt{2Qh/100}

$$P = \sqrt { \frac { 2 Q h } { 100 } }$$

Solve for Q

$$\left\{\begin{matrix}Q=\frac{50P^{2}}{h}\text{, }&P\geq 0\text{ and }h\neq 0\\Q\in \mathrm{R}\text{, }&h=0\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Radical Equations

Divide 2Qh by 100 to get \frac{1}{50}Qh.

$$P=\sqrt{\frac{1}{50}Qh}$$

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

$$\sqrt{\frac{1}{50}Qh}=P$$

Square both sides of the equation.

$$\frac{h}{50}Q=P^{2}$$

Divide both sides by \frac{1}{50}h.

$$\frac{50\times \frac{h}{50}Q}{h}=\frac{50P^{2}}{h}$$

Dividing by \frac{1}{50}h undoes the multiplication by \frac{1}{50}h.

$$Q=\frac{50P^{2}}{h}$$

Solve for P (complex solution)

$$P=\frac{\sqrt{2Qh}}{10}$$

Solve for Q (complex solution)

$$\left\{\begin{matrix}Q=\frac{50P^{2}}{h}\text{, }&h\neq 0\text{ and }\left(P=0\text{ or }arg(P)<\pi \right)\\Q\in \mathrm{C}\text{, }&P=0\text{ and }h=0\end{matrix}\right.$$

Solve for P

$$P=\frac{\sqrt{2Qh}}{10}$$

$$\left(h\geq 0\text{ and }Q\geq 0\right)\text{ or }\left(Q\leq 0\text{ and }h\leq 0\right)$$