Solve y=a*sqrt{b}

$$y = a \times \sqrt { b }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=b^{-\frac{1}{2}}y\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&y=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a\sqrt{b}=y$$

The equation is in standard form.

$$\sqrt{b}a=y$$

Divide both sides by \sqrt{b}.

$$\frac{\sqrt{b}a}{\sqrt{b}}=\frac{y}{\sqrt{b}}$$

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

$$a=\frac{y}{\sqrt{b}}$$

Divide y by \sqrt{b}.

$$a=b^{-\frac{1}{2}}y$$

Solve for a

$$\left\{\begin{matrix}a=\frac{y}{\sqrt{b}}\text{, }&b>0\\a\in \mathrm{R}\text{, }&b=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a\sqrt{b}=y$$

The equation is in standard form.

$$\sqrt{b}a=y$$

Divide both sides by \sqrt{b}.

$$\frac{\sqrt{b}a}{\sqrt{b}}=\frac{y}{\sqrt{b}}$$

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

$$a=\frac{y}{\sqrt{b}}$$

Solve for b

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

Steps for Solving Radical Equations

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

$$a\sqrt{b}=y$$

Divide both sides by a.

$$\frac{a\sqrt{b}}{a}=\frac{y}{a}$$

Dividing by a undoes the multiplication by a.

$$\sqrt{b}=\frac{y}{a}$$

Square both sides of the equation.

$$b=\frac{y^{2}}{a^{2}}$$

Solve for b (complex solution)

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