Solve frac{sqrt{2}}{5}-(1/2-frac{sqrt{3}}{3})

$$\frac{ \sqrt{ 2 } }{ 5 } -( \frac{ 1 }{ 2 } - \frac{ \sqrt{ 3 } }{ 3 } )$$

Evaluate

$$\frac{\sqrt{2}}{5}+\frac{\sqrt{3}}{3}-\frac{1}{2}\approx 0.360192982$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{1}{2} times \frac{3}{3}. Multiply \frac{\sqrt{3}}{3} times \frac{2}{2}.

$$\frac{\sqrt{2}}{5}-\left(\frac{3}{6}-\frac{2\sqrt{3}}{6}\right)$$

Since \frac{3}{6} and \frac{2\sqrt{3}}{6} have the same denominator, subtract them by subtracting their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 6 is 30. Multiply \frac{\sqrt{2}}{5} times \frac{6}{6}. Multiply \frac{3-2\sqrt{3}}{6} times \frac{5}{5}.

$$\frac{6\sqrt{2}}{30}-\frac{5\left(3-2\sqrt{3}\right)}{30}$$

Since \frac{6\sqrt{2}}{30} and \frac{5\left(3-2\sqrt{3}\right)}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\sqrt{2}-5\left(3-2\sqrt{3}\right)}{30}$$

Do the multiplications in 6\sqrt{2}-5\left(3-2\sqrt{3}\right).

$$\frac{6\sqrt{2}-15+10\sqrt{3}}{30}$$

Factor

$$\frac{6 \sqrt{2} + 10 \sqrt{3} - 15}{30} = 0.36019298166424474$$