Solve Q=Ksqrt{P}

$$Q = K \sqrt{ P }$$

Solve for K

$$\left\{\begin{matrix}K=\frac{Q}{\sqrt{P}}\text{, }&P>0\\K\in \mathrm{R}\text{, }&P=0\text{ and }Q=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$K\sqrt{P}=Q$$

The equation is in standard form.

$$\sqrt{P}K=Q$$

Divide both sides by \sqrt{P}.

$$\frac{\sqrt{P}K}{\sqrt{P}}=\frac{Q}{\sqrt{P}}$$

Dividing by \sqrt{P} undoes the multiplication by \sqrt{P}.

$$K=\frac{Q}{\sqrt{P}}$$

Solve for P

$$\left\{\begin{matrix}P=\left(\frac{Q}{K}\right)^{2}\text{, }&\left(Q\geq 0\text{ and }K>0\right)\text{ or }\left(Q\leq 0\text{ and }K<0\right)\\P\geq 0\text{, }&Q=0\text{ and }K=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$K\sqrt{P}=Q$$

Divide both sides by K.

$$\frac{K\sqrt{P}}{K}=\frac{Q}{K}$$

Dividing by K undoes the multiplication by K.

$$\sqrt{P}=\frac{Q}{K}$$

Square both sides of the equation.

$$P=\frac{Q^{2}}{K^{2}}$$