Solve 3/4-sqrt{2}+sqrt{6}*frac{sqrt{3}}{3}

$$\frac { 3 } { 4 } - \sqrt { 2 } + \sqrt { 6 } \times \frac { \sqrt { 3 } } { 3 }$$

Evaluate

$$\frac{3}{4}=0.75$$

Short Solution Steps

Express \sqrt{6}\times \frac{\sqrt{3}}{3} as a single fraction.

$$\frac{3}{4}-\sqrt{2}+\frac{\sqrt{6}\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{3}{4} times \frac{3}{3}. Multiply \frac{\sqrt{6}\sqrt{3}}{3} times \frac{4}{4}.

$$\frac{3\times 3}{12}-\sqrt{2}+\frac{4\sqrt{6}\sqrt{3}}{12}$$

Since \frac{3\times 3}{12} and \frac{4\sqrt{6}\sqrt{3}}{12} have the same denominator, add them by adding their numerators.

$$\frac{3\times 3+4\sqrt{6}\sqrt{3}}{12}-\sqrt{2}$$

Do the multiplications in 3\times 3+4\sqrt{6}\sqrt{3}.

$$\frac{9+12\sqrt{2}}{12}-\sqrt{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{2} times \frac{12}{12}.

$$\frac{9+12\sqrt{2}}{12}-\frac{12\sqrt{2}}{12}$$

Since \frac{9+12\sqrt{2}}{12} and \frac{12\sqrt{2}}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9+12\sqrt{2}-12\sqrt{2}}{12}$$

Do the calculations in 9+12\sqrt{2}-12\sqrt{2}.

$$\frac{9}{12}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$