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

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

Evaluate

$$\frac{\sqrt{6}}{3}+\sqrt{3}-1\approx 1.548547388$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

$$\frac{\sqrt{2}}{\sqrt{3}}-\left(1-\sqrt{3}\right)$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\left(1-\sqrt{3}\right)$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{3}-\left(1-\sqrt{3}\right)$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{3}-\left(1-\sqrt{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1-\sqrt{3} times \frac{3}{3}.

$$\frac{\sqrt{6}}{3}-\frac{3\left(1-\sqrt{3}\right)}{3}$$

Since \frac{\sqrt{6}}{3} and \frac{3\left(1-\sqrt{3}\right)}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{6}-3\left(1-\sqrt{3}\right)}{3}$$

Do the multiplications in \sqrt{6}-3\left(1-\sqrt{3}\right).

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