Solve 1/x=sqrt{1/2}

$$\frac{ 1 }{ x } = \sqrt{ \frac{ 1 }{ 2 } }$$

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

Steps for Solving Linear Equation

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

$$1=x\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$1=x\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$1=x\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$1=x\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$1=x\times \frac{\sqrt{2}}{2}$$

Express x\times \frac{\sqrt{2}}{2} as a single fraction.

$$1=\frac{x\sqrt{2}}{2}$$

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

$$\frac{x\sqrt{2}}{2}=1$$

Multiply both sides by 2.

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

The equation is in standard form.

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

Divide both sides by \sqrt{2}.

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

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

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

Divide 2 by \sqrt{2}.

$$x=\sqrt{2}$$