Solve =4(frac{sqrt{3}}{2})+1-3sqrt{2}div2

$$= 4 ( \frac { \sqrt { 3 } } { 2 } ) + 1 - 3 \sqrt { 2 } \div 2$$

Evaluate

$$-\frac{3\sqrt{2}}{2}+2\sqrt{3}+1\approx 2.342781272$$

Short Solution Steps

Cancel out 2, the greatest common factor in 4 and 2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{3}+1 times \frac{2}{2}.

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

Since \frac{2\left(2\sqrt{3}+1\right)}{2} and \frac{3\sqrt{2}}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\left(2\sqrt{3}+1\right)-3\sqrt{2}.

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

Factor

$$\frac{4 \sqrt{3} + 2 - 3 \sqrt{2}}{2} = 2.3427812715781116$$