Solve frac{3sqrt{2}}{2}-sqrt{1/3}

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

Evaluate

$$\frac{3\sqrt{2}}{2}-\frac{\sqrt{3}}{3}\approx 1.543970074$$

Short Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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

Do the multiplications in 3\times 3\sqrt{2}-2\sqrt{3}.

$$\frac{9\sqrt{2}-2\sqrt{3}}{6}$$

Factor

$$\frac{9 \sqrt{2} - 2 \sqrt{3}}{6} = 1.5439700743700169$$