Selesaikan 3/4sqrt{3}-2/5sqrt{5}+6/7sqrt{2}-4/3sqrt{2}+frac{5}{2}sqrt{3}-frac{7}{6}sqrt{5}

$$\frac{ 3 }{ 4 } \sqrt{ 3 } - \frac{ 2 }{ 5 } \sqrt{ 5 } + \frac{ 6 }{ 7 } \sqrt{ 2 } - \frac{ 4 }{ 3 } \sqrt{ 2 } + \frac{ 5 }{ 2 } \sqrt{ 3 } - \frac{ 7 }{ 6 } \sqrt{ 5 }$$

Nilaikan

$$\frac{13\sqrt{3}}{4}-\frac{10\sqrt{2}}{21}-\frac{47\sqrt{5}}{30}\approx 1.45255693$$

Langkah Penyelesaian

Gabungkan \frac{6}{7}\sqrt{2} dan -\frac{4}{3}\sqrt{2} untuk mendapatkan -\frac{10}{21}\sqrt{2}.

$$\frac{3}{4}\sqrt{3}-\frac{2}{5}\sqrt{5}-\frac{10}{21}\sqrt{2}+\frac{5}{2}\sqrt{3}-\frac{7}{6}\sqrt{5}$$

Gabungkan \frac{3}{4}\sqrt{3} dan \frac{5}{2}\sqrt{3} untuk mendapatkan \frac{13}{4}\sqrt{3}.

$$\frac{13}{4}\sqrt{3}-\frac{2}{5}\sqrt{5}-\frac{10}{21}\sqrt{2}-\frac{7}{6}\sqrt{5}$$

Gabungkan -\frac{2}{5}\sqrt{5} dan -\frac{7}{6}\sqrt{5} untuk mendapatkan -\frac{47}{30}\sqrt{5}.

$$\frac{13}{4}\sqrt{3}-\frac{47}{30}\sqrt{5}-\frac{10}{21}\sqrt{2}$$

Faktor

$$\frac{1365 \sqrt{3} - 200 \sqrt{2} - 658 \sqrt{5}}{420} = 1.4525569301477066$$