Løs sqrt{2}-frac{sqrt{3}}{2}+frac{sqrt{2}}{3}-frac{sqrt{3}}{5}+3sqrt{3}+2sqrt{2}

$$\sqrt { 2 } - \frac { \sqrt { 3 } } { 2 } + \frac { \sqrt { 2 } } { 3 } - \frac { \sqrt { 3 } } { 5 } + 3 \sqrt { 3 } + 2 \sqrt { 2 }$$

Evaluer

$$\frac{10\sqrt{2}}{3}+\frac{23\sqrt{3}}{10}\approx 8,697762065$$

Løsningsvejledning

Kombiner \sqrt{2} og \frac{\sqrt{2}}{3} for at få \frac{4}{3}\sqrt{2}.

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

Kombiner -\frac{\sqrt{3}}{2} og -\frac{\sqrt{3}}{5} for at få -\frac{7}{10}\sqrt{3}.

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

Kombiner -\frac{7}{10}\sqrt{3} og 3\sqrt{3} for at få \frac{23}{10}\sqrt{3}.

$$\frac{4}{3}\sqrt{2}+\frac{23}{10}\sqrt{3}+2\sqrt{2}$$

Kombiner \frac{4}{3}\sqrt{2} og 2\sqrt{2} for at få \frac{10}{3}\sqrt{2}.

$$\frac{10}{3}\sqrt{2}+\frac{23}{10}\sqrt{3}$$

Faktoriser

$$\frac{69 \sqrt{3} + 100 \sqrt{2}}{30} = 8,697762065318734$$