Solve (sqrt{2}d-2sqrt{3})divsqrt{3}

$$( \sqrt { 2 } d - 2 \sqrt { 3 } ) \div \sqrt { 3 }$$

Evaluate

$$\frac{\sqrt{6}d}{3}-2$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

$$\frac{\left(\sqrt{2}d-2\sqrt{3}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply \sqrt{2}d-2\sqrt{3} by \sqrt{3}.

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

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

$$\frac{\sqrt{6}d-2\left(\sqrt{3}\right)^{2}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{6}d-2\times 3}{3}$$

Multiply -2 and 3 to get -6.

$$\frac{\sqrt{6}d-6}{3}$$

Differentiate w.r.t. d

$$\frac{\sqrt{6}}{3} = 0.8164965809277259$$