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

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

Evalueren

$$\frac{13\sqrt{3}}{4}-\frac{10\sqrt{2}}{21}-\frac{47\sqrt{5}}{30}\approx 1,45255693$$

Oplossingsstappen

Combineer \frac{6}{7}\sqrt{2} en -\frac{4}{3}\sqrt{2} om -\frac{10}{21}\sqrt{2} te krijgen.

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

Combineer \frac{3}{4}\sqrt{3} en \frac{5}{2}\sqrt{3} om \frac{13}{4}\sqrt{3} te krijgen.

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

Combineer -\frac{2}{5}\sqrt{5} en -\frac{7}{6}\sqrt{5} om -\frac{47}{30}\sqrt{5} te krijgen.

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

Factoriseren

$$\frac{1365 \sqrt{3} - 200 \sqrt{2} - 658 \sqrt{5}}{420} = 1,4525569301477066$$