Solve (2+1/9-1/3)sqrt{3}

$$( 2 + \frac { 1 } { 9 } - \frac { 1 } { 3 } ) \sqrt { 3 }$$

Evaluate

$$\frac{16\sqrt{3}}{9}\approx 3.079201436$$

Solution Steps

Convert 2 to fraction \frac{18}{9}.

$$\left(\frac{18}{9}+\frac{1}{9}-\frac{1}{3}\right)\sqrt{3}$$

Since \frac{18}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\left(\frac{18+1}{9}-\frac{1}{3}\right)\sqrt{3}$$

Add 18 and 1 to get 19.

$$\left(\frac{19}{9}-\frac{1}{3}\right)\sqrt{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{19}{9} and \frac{1}{3} to fractions with denominator 9.

$$\left(\frac{19}{9}-\frac{3}{9}\right)\sqrt{3}$$

Since \frac{19}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-3}{9}\sqrt{3}$$

Subtract 3 from 19 to get 16.

$$\frac{16}{9}\sqrt{3}$$