Solve 3x=9/13sqrt{13}*12/13sqrt{39}

$$3 x = \frac { 9 } { 13 } \sqrt { 13 } \times \frac { 12 } { 13 } \sqrt { 39 }$$

Solve for x

$$x = \frac{36 \sqrt{3}}{13} \approx 4.79644839$$

Steps for Solving Linear Equation

Factor 39=13\times 3. Rewrite the square root of the product \sqrt{13\times 3} as the product of square roots \sqrt{13}\sqrt{3}.

$$3x=\frac{9}{13}\sqrt{13}\times \frac{12}{13}\sqrt{13}\sqrt{3}$$

Multiply \sqrt{13} and \sqrt{13} to get 13.

$$3x=\frac{9}{13}\times 13\times \frac{12}{13}\sqrt{3}$$

Cancel out 13 and 13.

$$3x=9\times \frac{12}{13}\sqrt{3}$$

Express 9\times \frac{12}{13} as a single fraction.

$$3x=\frac{9\times 12}{13}\sqrt{3}$$

Multiply 9 and 12 to get 108.

$$3x=\frac{108}{13}\sqrt{3}$$

The equation is in standard form.

$$3x=\frac{108\sqrt{3}}{13}$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{108\sqrt{3}}{3\times 13}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{108\sqrt{3}}{3\times 13}$$

Divide \frac{108\sqrt{3}}{13} by 3.

$$x=\frac{36\sqrt{3}}{13}$$