Solve 1+frac{frac{frac{sqrt{5}}{2}}{3}}{2}

$$1+ \frac{ \frac{ \frac{ \sqrt{ 5 } }{ 2 } }{ 3 } }{ 2 }$$

Evaluate

$$\frac{\sqrt{5}}{12}+1\approx 1.186338998$$

Solution Steps

Express \frac{\frac{\frac{\sqrt{5}}{2}}{3}}{2} as a single fraction.

$$1+\frac{\frac{\sqrt{5}}{2}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$1+\frac{\frac{\sqrt{5}}{2}}{6}$$

Express \frac{\frac{\sqrt{5}}{2}}{6} as a single fraction.

$$1+\frac{\sqrt{5}}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$1+\frac{\sqrt{5}}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{12}{12}.

$$\frac{12}{12}+\frac{\sqrt{5}}{12}$$

Since \frac{12}{12} and \frac{\sqrt{5}}{12} have the same denominator, add them by adding their numerators.

$$\frac{12+\sqrt{5}}{12}$$

Factor

$$\frac{\sqrt{5} + 12}{12} = 1.1863389981249826$$