Lahenda (frac{sqrt{5}}{sqrt{6}}-frac{sqrt{2}}{sqrt{15}})^2

$$( \frac { \sqrt { 5 } } { \sqrt { 6 } } - \frac { \sqrt { 2 } } { \sqrt { 15 } } ) ^ { 2 }$$

Arvuta

$$\frac{3}{10}=0,3$$

Lahenduse etapid

Ratsionaliseerige korrutades lugeja ja \sqrt{6} nimetaja \frac{\sqrt{5}}{\sqrt{6}} nimetaja.

$$\left(\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}-\frac{\sqrt{2}}{\sqrt{15}}\right)^{2}$$

\sqrt{6} ruut on 6.

$$\left(\frac{\sqrt{5}\sqrt{6}}{6}-\frac{\sqrt{2}}{\sqrt{15}}\right)^{2}$$

\sqrt{5} ja \sqrt{6} korrutage numbrid, mis on sama juur.

$$\left(\frac{\sqrt{30}}{6}-\frac{\sqrt{2}}{\sqrt{15}}\right)^{2}$$

Ratsionaliseerige korrutades lugeja ja \sqrt{15} nimetaja \frac{\sqrt{2}}{\sqrt{15}} nimetaja.

$$\left(\frac{\sqrt{30}}{6}-\frac{\sqrt{2}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}\right)^{2}$$

\sqrt{15} ruut on 15.

$$\left(\frac{\sqrt{30}}{6}-\frac{\sqrt{2}\sqrt{15}}{15}\right)^{2}$$

\sqrt{2} ja \sqrt{15} korrutage numbrid, mis on sama juur.

$$\left(\frac{\sqrt{30}}{6}-\frac{\sqrt{30}}{15}\right)^{2}$$

Kombineerige \frac{\sqrt{30}}{6} ja -\frac{\sqrt{30}}{15}, et leida \frac{1}{10}\sqrt{30}.

$$\left(\frac{1}{10}\sqrt{30}\right)^{2}$$

Laiendage \left(\frac{1}{10}\sqrt{30}\right)^{2}.

$$\left(\frac{1}{10}\right)^{2}\left(\sqrt{30}\right)^{2}$$

Arvutage 2 aste \frac{1}{10} ja leidke \frac{1}{100}.

$$\frac{1}{100}\left(\sqrt{30}\right)^{2}$$

\sqrt{30} ruut on 30.

$$\frac{1}{100}\times 30$$

Korrutage \frac{1}{100} ja 30, et leida \frac{3}{10}.

$$\frac{3}{10}$$

Lahuta teguriteks

$$\frac{3}{2 \cdot 5} = 0,3$$