Solve x/3sqrt{2}=frac{sqrt{5}}{sqrt{10}}

$$\frac { x } { 3 \sqrt { 2 } } = \frac { \sqrt { 5 } } { \sqrt { 10 } }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{x\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}=\frac{\sqrt{5}}{\sqrt{10}}$$

The square of \sqrt{2} is 2.

$$\frac{x\sqrt{2}}{3\times 2}=\frac{\sqrt{5}}{\sqrt{10}}$$

Multiply 3 and 2 to get 6.

$$\frac{x\sqrt{2}}{6}=\frac{\sqrt{5}}{\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{x\sqrt{2}}{6}=\frac{\sqrt{5}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{x\sqrt{2}}{6}=\frac{\sqrt{5}\sqrt{10}}{10}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\frac{x\sqrt{2}}{6}=\frac{\sqrt{5}\sqrt{5}\sqrt{2}}{10}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{x\sqrt{2}}{6}=\frac{5\sqrt{2}}{10}$$

Divide 5\sqrt{2} by 10 to get \frac{1}{2}\sqrt{2}.

$$\frac{x\sqrt{2}}{6}=\frac{1}{2}\sqrt{2}$$

Multiply both sides of the equation by 6, the least common multiple of 6,2.

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

The equation is in standard form.

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

Divide both sides by \sqrt{2}.

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

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

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

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

$$x=3$$