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

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

Solve for D

$$D=300$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10.

$$20\times \frac{\sqrt{5}}{\sqrt{2}}=\frac{D}{3\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$20\times \frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\frac{D}{3\sqrt{10}}$$

The square of \sqrt{2} is 2.

$$20\times \frac{\sqrt{5}\sqrt{2}}{2}=\frac{D}{3\sqrt{10}}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$20\times \frac{\sqrt{10}}{2}=\frac{D}{3\sqrt{10}}$$

Cancel out 2, the greatest common factor in 20 and 2.

$$10\sqrt{10}=\frac{D}{3\sqrt{10}}$$

Rationalize the denominator of \frac{D}{3\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

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

The square of \sqrt{10} is 10.

$$10\sqrt{10}=\frac{D\sqrt{10}}{3\times 10}$$

Multiply 3 and 10 to get 30.

$$10\sqrt{10}=\frac{D\sqrt{10}}{30}$$

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

$$\frac{D\sqrt{10}}{30}=10\sqrt{10}$$

Multiply both sides of the equation by 30.

$$D\sqrt{10}=300\sqrt{10}$$

The equation is in standard form.

$$\sqrt{10}D=300\sqrt{10}$$

Divide both sides by \sqrt{10}.

$$\frac{\sqrt{10}D}{\sqrt{10}}=\frac{300\sqrt{10}}{\sqrt{10}}$$

Dividing by \sqrt{10} undoes the multiplication by \sqrt{10}.

$$D=\frac{300\sqrt{10}}{\sqrt{10}}$$

Divide 300\sqrt{10} by \sqrt{10}.

$$D=300$$