Solve sqrt{ax}=z

$$\sqrt{ ax } = z$$

Solve for a

$$\left\{\begin{matrix}a=\frac{z^{2}}{x}\text{, }&z\geq 0\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$xa=z^{2}$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{z^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{z^{2}}{x}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{z^{2}}{a}\text{, }&z\geq 0\text{ and }a\neq 0\\x\in \mathrm{R}\text{, }&z=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$ax=z^{2}$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{z^{2}}{a}$$

Dividing by a undoes the multiplication by a.

$$x=\frac{z^{2}}{a}$$

Solve for a (complex solution)

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

Solve for x (complex solution)

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