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

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

Evaluate

$$\frac{\sqrt{3}+3}{4}\approx 1.183012702$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1+1\sqrt{3}}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2+1+1\sqrt{3}.

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

Do the calculations in 2+1+\sqrt{3}.

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

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

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

Multiply 2 and 2 to get 4.

$$\frac{3+\sqrt{3}}{4}$$

Factor

$$\frac{\sqrt{3} {(\sqrt{3} + 1)}}{4} = 1.1830127018922192$$