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

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

Luacháil

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

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{6} chun ainmneoir \frac{\sqrt{5}}{\sqrt{6}} a thiontú in uimhir chóimheasta.

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

Is é 6 uimhir chearnach \sqrt{6}.

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

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{5} agus \sqrt{6} a iolrú.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{15} chun ainmneoir \frac{\sqrt{2}}{\sqrt{15}} a thiontú in uimhir chóimheasta.

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

Is é 15 uimhir chearnach \sqrt{15}.

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

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{2} agus \sqrt{15} a iolrú.

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

Comhcheangail \frac{\sqrt{30}}{6} agus -\frac{\sqrt{30}}{15} chun \frac{1}{10}\sqrt{30} a fháil.

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

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

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

Ríomh cumhacht \frac{1}{10} de 2 agus faigh \frac{1}{100}.

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

Is é 30 uimhir chearnach \sqrt{30}.

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

Méadaigh \frac{1}{100} agus 30 chun \frac{3}{10} a fháil.

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

Fachtóirigh

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