Solve 2+4/9-1+sqrt{1/3}

$$2 + \frac { 4 } { 9 } - 1 + \sqrt { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{\sqrt{3}}{3}+\frac{13}{9}\approx 2.021794714$$

Short Solution Steps

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

$$\frac{18}{9}+\frac{4}{9}-1+\sqrt{\frac{1}{3}}$$

Since \frac{18}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{18+4}{9}-1+\sqrt{\frac{1}{3}}$$

Add 18 and 4 to get 22.

$$\frac{22}{9}-1+\sqrt{\frac{1}{3}}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{22}{9}-\frac{9}{9}+\sqrt{\frac{1}{3}}$$

Since \frac{22}{9} and \frac{9}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-9}{9}+\sqrt{\frac{1}{3}}$$

Subtract 9 from 22 to get 13.

$$\frac{13}{9}+\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{13}{9}+\frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$\frac{13}{9}+\frac{1}{\sqrt{3}}$$

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

$$\frac{13}{9}+\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{13}{9}+\frac{\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 3 is 9. Multiply \frac{\sqrt{3}}{3} times \frac{3}{3}.

$$\frac{13}{9}+\frac{3\sqrt{3}}{9}$$

Since \frac{13}{9} and \frac{3\sqrt{3}}{9} have the same denominator, add them by adding their numerators.

$$\frac{13+3\sqrt{3}}{9}$$

Factor

$$\frac{3 \sqrt{3} + 13}{9} = 2.0217947136340704$$