Solve D=sqrt{3N}R

$$D = \sqrt { 3 N } R$$

Solve for N

$$\left\{\begin{matrix}N=\frac{\left(\frac{D}{R}\right)^{2}}{3}\text{, }&\left(D\geq 0\text{ and }R>0\right)\text{ or }\left(D\leq 0\text{ and }R<0\right)\\N\geq 0\text{, }&D=0\text{ and }R=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{3N}R=D$$

Divide both sides by R.

$$\frac{R\sqrt{3N}}{R}=\frac{D}{R}$$

Dividing by R undoes the multiplication by R.

$$\sqrt{3N}=\frac{D}{R}$$

Square both sides of the equation.

$$3N=\frac{D^{2}}{R^{2}}$$

Divide both sides by 3.

$$\frac{3N}{3}=\frac{D^{2}}{3R^{2}}$$

Dividing by 3 undoes the multiplication by 3.

$$N=\frac{D^{2}}{3R^{2}}$$

Solve for D

$$D=\sqrt{3N}R$$

$$N\geq 0$$