Lutasin ang frac{frac{sqrt{3}}{2}-18+10sqrt{3}}{sqrt{3}}

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

I-evaluate

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

Mga Hakbang ng Solution

Pagsamahin ang \frac{\sqrt{3}}{2} at 10\sqrt{3} para makuha ang \frac{21}{2}\sqrt{3}.

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

I-rationalize ang denominator ng \frac{\frac{21}{2}\sqrt{3}-18}{\sqrt{3}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{3}.

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

Ang square ng \sqrt{3} ay 3.

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

Gamitin ang distributive property para i-multiply ang \frac{21}{2}\sqrt{3}-18 gamit ang \sqrt{3}.

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

I-multiply ang \sqrt{3} at \sqrt{3} para makuha ang 3.

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

Ipakita ang \frac{21}{2}\times 3 bilang isang single fraction.

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

I-multiply ang 21 at 3 para makuha ang 63.

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

I-factor

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