Solve 9divx=sqrt{3div2}

$$9 \div x= \sqrt{ 3 \div 2 }$$

Solve for x

$$x=3\sqrt{6}\approx 7.348469228$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$9=x\sqrt{\frac{3}{2}}$$

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$9=x\times \frac{\sqrt{3}}{\sqrt{2}}$$

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

$$9=x\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$9=x\times \frac{\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$9=x\times \frac{\sqrt{6}}{2}$$

Express x\times \frac{\sqrt{6}}{2} as a single fraction.

$$9=\frac{x\sqrt{6}}{2}$$

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

$$\frac{x\sqrt{6}}{2}=9$$

Multiply both sides by 2.

$$x\sqrt{6}=9\times 2$$

Multiply 9 and 2 to get 18.

$$x\sqrt{6}=18$$

The equation is in standard form.

$$\sqrt{6}x=18$$

Divide both sides by \sqrt{6}.

$$\frac{\sqrt{6}x}{\sqrt{6}}=\frac{18}{\sqrt{6}}$$

Dividing by \sqrt{6} undoes the multiplication by \sqrt{6}.

$$x=\frac{18}{\sqrt{6}}$$

Divide 18 by \sqrt{6}.

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