Solve frac{sqrt{17}+3}{2}*sqrt{3}-3sqrt{3}

$$\frac{ \sqrt{ 17 } +3 }{ 2 } \times \sqrt{ 3 } -3 \sqrt{ 3 }$$

Evaluate

$$\frac{\sqrt{3}\left(\sqrt{17}-3\right)}{2}\approx 0.972638003$$

Short Solution Steps

Express \frac{\sqrt{17}+3}{2}\sqrt{3} as a single fraction.

$$\frac{\left(\sqrt{17}+3\right)\sqrt{3}}{2}-3\sqrt{3}$$

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

$$\frac{\left(\sqrt{17}+3\right)\sqrt{3}}{2}+\frac{2\left(-3\right)\sqrt{3}}{2}$$

Since \frac{\left(\sqrt{17}+3\right)\sqrt{3}}{2} and \frac{2\left(-3\right)\sqrt{3}}{2} have the same denominator, add them by adding their numerators.

$$\frac{\left(\sqrt{17}+3\right)\sqrt{3}+2\left(-3\right)\sqrt{3}}{2}$$

Do the multiplications in \left(\sqrt{17}+3\right)\sqrt{3}+2\left(-3\right)\sqrt{3}.

$$\frac{\sqrt{51}+3\sqrt{3}-6\sqrt{3}}{2}$$

Do the calculations in \sqrt{51}+3\sqrt{3}-6\sqrt{3}.

$$\frac{-3\sqrt{3}+\sqrt{51}}{2}$$

Factor

$$\frac{\sqrt{3} {(\sqrt{17} - 3)}}{2} = 0.972638002918109$$