Solve frac{frac{sqrt{3}}{2}-18+10sqrt{3}}{sqrt{3}}

$$\frac{ \frac{ \sqrt{ 3 } }{ 2 } -18+10 \sqrt{ 3 } }{ \sqrt{ 3 } }$$

Evaluate

$$\frac{21}{2}-6\sqrt{3}\approx 0.107695155$$

Solution Steps

Combine \frac{\sqrt{3}}{2} and 10\sqrt{3} to get \frac{21}{2}\sqrt{3}.

$$\frac{\frac{21}{2}\sqrt{3}-18}{\sqrt{3}}$$

Rationalize the denominator of \frac{\frac{21}{2}\sqrt{3}-18}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(\frac{21}{2}\sqrt{3}-18\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(\frac{21}{2}\sqrt{3}-18\right)\sqrt{3}}{3}$$

Use the distributive property to multiply \frac{21}{2}\sqrt{3}-18 by \sqrt{3}.

$$\frac{\frac{21}{2}\sqrt{3}\sqrt{3}-18\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{\frac{21}{2}\times 3-18\sqrt{3}}{3}$$

Express \frac{21}{2}\times 3 as a single fraction.

$$\frac{\frac{21\times 3}{2}-18\sqrt{3}}{3}$$

Multiply 21 and 3 to get 63.

$$\frac{\frac{63}{2}-18\sqrt{3}}{3}$$

Factor

$$\frac{3 {(7 - 4 \sqrt{3})}}{2} = 0.10769515458673684$$