Solve x/sqrt{2}=sqrt{32}

$$\frac { x } { \sqrt { 2 } } = \sqrt { 32 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

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

$$\frac{x\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\sqrt{32}$$

The square of \sqrt{2} is 2.

$$\frac{x\sqrt{2}}{2}=\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{x\sqrt{2}}{2}=4\sqrt{2}$$

Multiply both sides of the equation by 2.

$$x\sqrt{2}=8\sqrt{2}$$

The equation is in standard form.

$$\sqrt{2}x=8\sqrt{2}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{8\sqrt{2}}{\sqrt{2}}$$

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

$$x=\frac{8\sqrt{2}}{\sqrt{2}}$$

Divide 8\sqrt{2} by \sqrt{2}.

$$x=8$$