Solve 3/2*3sqrt{3}-frac{sqrt{3}*(3/2)^2}{4}

$$\frac { 3 } { 2 } \times 3 \sqrt { 3 } - \frac { \sqrt { 3 } \times ( \frac { 3 } { 2 } ) ^ { 2 } } { 4 }$$

Evaluate

$$\frac{63\sqrt{3}}{16}\approx 6.819950055$$

Solution Steps

Express 3\times \frac{3}{2} as a single fraction.

$$\frac{3\times 3}{2}\sqrt{3}-\frac{\sqrt{3}\times \left(\frac{3}{2}\right)^{2}}{4}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{2}\sqrt{3}-\frac{\sqrt{3}\times \left(\frac{3}{2}\right)^{2}}{4}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{2}\sqrt{3}-\frac{\sqrt{3}\times \frac{9}{4}}{4}$$

Divide \sqrt{3}\times \frac{9}{4} by 4 to get \sqrt{3}\times \frac{9}{16}.

$$\frac{9}{2}\sqrt{3}-\sqrt{3}\times \frac{9}{16}$$

Multiply -1 and \frac{9}{16} to get -\frac{9}{16}.

$$\frac{9}{2}\sqrt{3}-\frac{9}{16}\sqrt{3}$$

Combine \frac{9}{2}\sqrt{3} and -\frac{9}{16}\sqrt{3} to get \frac{63}{16}\sqrt{3}.

$$\frac{63}{16}\sqrt{3}$$