Solve frac{sqrt{2}}{sqrt{3}}x1/2

$$\frac { \sqrt { 2 } } { \sqrt { 3 } } x \frac { 1 } { 2 }$$

Evaluate

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

Solution Steps

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

$$\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}x\times \frac{1}{2}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{3}x\times \frac{1}{2}$$

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

$$\frac{\sqrt{6}}{3}x\times \frac{1}{2}$$

Express \frac{\sqrt{6}}{3}x as a single fraction.

$$\frac{\sqrt{6}x}{3}\times \frac{1}{2}$$

Multiply \frac{\sqrt{6}x}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 3 and 2 to get 6.

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

Differentiate w.r.t. x

$$\frac{\sqrt{6}}{6} = 0.40824829046386296$$