Solve sqrt{2}=a/b

$$\sqrt { 2 } = \frac { a } { b }$$

Solve for a

$$a=\sqrt{2}b$$

$$b\neq 0$$

Solution Steps

Multiply both sides of the equation by b.

$$b\sqrt{2}=a$$

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

$$a=b\sqrt{2}$$

Solve for b

$$b=\frac{\sqrt{2}a}{2}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.

$$b\sqrt{2}=a$$

The equation is in standard form.

$$\sqrt{2}b=a$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}b}{\sqrt{2}}=\frac{a}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$b=\frac{a}{\sqrt{2}}$$

Divide a by \sqrt{2}.

$$b=\frac{\sqrt{2}a}{2}$$

Variable b cannot be equal to 0.

$$b=\frac{\sqrt{2}a}{2}\text{, }b\neq 0$$