Solve frac{frac{sqrt{3}+1}{2}}{sqrt{3}}

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

Evaluate

$$\frac{\sqrt{3}}{6}+\frac{1}{2}\approx 0.788675135$$

Solution Steps

Express \frac{\frac{\sqrt{3}+1}{2}}{\sqrt{3}} as a single fraction.

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

Rationalize the denominator of \frac{\sqrt{3}+1}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

$$\frac{\left(\sqrt{3}+1\right)\sqrt{3}}{6}$$

Use the distributive property to multiply \sqrt{3}+1 by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{3+\sqrt{3}}{6}$$