Solve sqrt{3}=x/sqrt{2}

$$\sqrt { 3 } = \frac { x } { \sqrt { 2 } }$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\sqrt{3}=\frac{x\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{3}=\frac{x\sqrt{2}}{2}$$

Multiply both sides of the equation by 2.

$$2\sqrt{3}=x\sqrt{2}$$

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

$$x\sqrt{2}=2\sqrt{3}$$

The equation is in standard form.

$$\sqrt{2}x=2\sqrt{3}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{2\sqrt{3}}{\sqrt{2}}$$

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

$$x=\frac{2\sqrt{3}}{\sqrt{2}}$$

Divide 2\sqrt{3} by \sqrt{2}.

$$x=\sqrt{6}$$