Solve 5/2-5/3sqrt{3}-3sqrt{3}+6

$$\frac { 5 } { 2 } - \frac { 5 } { 3 } \sqrt { 3 } - 3 \sqrt { 3 } + 6$$

Evaluate

$$-\frac{14\sqrt{3}}{3}+\frac{17}{2}\approx 0.417096231$$

Solution Steps

Combine -\frac{5}{3}\sqrt{3} and -3\sqrt{3} to get -\frac{14}{3}\sqrt{3}.

$$\frac{5}{2}-\frac{14}{3}\sqrt{3}+6$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{5}{2}-\frac{14}{3}\sqrt{3}+\frac{12}{2}$$

Since \frac{5}{2} and \frac{12}{2} have the same denominator, add them by adding their numerators.

$$\frac{5+12}{2}-\frac{14}{3}\sqrt{3}$$

Add 5 and 12 to get 17.

$$\frac{17}{2}-\frac{14}{3}\sqrt{3}$$

Factor

$$\frac{51 - 28 \sqrt{3}}{6} = 0.4170962313452395$$