Solve frac{1/3*sqrt{6}}{sqrt{3}}=xquadfrac{2sqrt{2}}{3}

$$\frac { \frac { 1 } { 3 } \cdot \sqrt { 6 } } { \sqrt { 3 } } = x \quad \frac { 2 \sqrt { 2 } } { 3 }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3^{\frac{1}{2}}\times \frac{1}{3}\sqrt{6}=x\times 2\sqrt{2}$$

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

$$x\times 2\sqrt{2}=3^{\frac{1}{2}}\times \frac{1}{3}\sqrt{6}$$

Reorder the terms.

$$2\sqrt{2}x=\frac{1}{3}\sqrt{3}\sqrt{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$2\sqrt{2}x=\frac{1}{3}\sqrt{3}\sqrt{3}\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\sqrt{2}x=\frac{1}{3}\times 3\sqrt{2}$$

Cancel out 3 and 3.

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

Divide both sides by 2\sqrt{2}.

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

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

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

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

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