Solve frac{2xfrac{sqrt{3}}{2}}{frac{sqrt{2}}{2}}

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

Evaluate

$$\sqrt{6}x$$

Solution Steps

Divide 2x\times \frac{\sqrt{3}}{2} by \frac{\sqrt{2}}{2} by multiplying 2x\times \frac{\sqrt{3}}{2} by the reciprocal of \frac{\sqrt{2}}{2}.

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

Multiply 2 and 2 to get 4.

$$\frac{4x\times \frac{\sqrt{3}}{2}}{\sqrt{2}}$$

Cancel out 2, the greatest common factor in 4 and 2.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Cancel out 2 and 2.

$$\sqrt{6}x$$

Differentiate w.r.t. x

$$\sqrt{6} = 2.449489743$$