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

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

Evalwa

$$\frac{3}{10}=0.3$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{5}}{\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}.

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

Il-kwadrat ta' \sqrt{6} huwa 6.

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

Biex timmultiplika \sqrt{5} u \sqrt{6}, immultiplika n-numri taħt l-għerq kwadrat.

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

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2}}{\sqrt{15}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{15}.

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

Il-kwadrat ta' \sqrt{15} huwa 15.

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

Biex timmultiplika \sqrt{2} u \sqrt{15}, immultiplika n-numri taħt l-għerq kwadrat.

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

Ikkombina \frac{\sqrt{30}}{6} u -\frac{\sqrt{30}}{15} biex tikseb \frac{1}{10}\sqrt{30}.

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

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

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

Ikkalkula \frac{1}{10} bil-power ta' 2 u tikseb \frac{1}{100}.

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

Il-kwadrat ta' \sqrt{30} huwa 30.

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

Immultiplika \frac{1}{100} u 30 biex tikseb \frac{3}{10}.

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

Fattur

$$\frac{3}{2 \cdot 5} = 0.3$$