Solve 2x=frac{3sqrt{6}}{sqrt{3}}

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

Solve for x

$$x = \frac{3 \sqrt{2}}{2} \approx 2.121320344$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{3\sqrt{6}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2x=\frac{3\sqrt{6}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

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}.

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

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

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

Cancel out 3 and 3.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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