Réitigh frac{sqrt{6}-sqrt{2}}{4}*frac{sqrt{6}-1sqrt{2}}{4}

$$\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 } \times \frac { \sqrt { 6 } - 1 \sqrt { 2 } } { 4 }$$

Luacháil

$$-\frac{\sqrt{3}}{4}+\frac{1}{2}\approx 0.066987298$$

Céimeanna Réitigh

Méadaigh \frac{\sqrt{6}-\sqrt{2}}{4} agus \frac{\sqrt{6}-\sqrt{2}}{4} chun \left(\frac{\sqrt{6}-\sqrt{2}}{4}\right)^{2} a fháil.

$$\left(\frac{\sqrt{6}-\sqrt{2}}{4}\right)^{2}$$

Chun \frac{\sqrt{6}-\sqrt{2}}{4} a iolrú i gcumhacht, iolraigh an t-uimhreoir agus an t-ainmneoir araon i gcumhacht agus déan iad a roinnt ansin.

$$\frac{\left(\sqrt{6}-\sqrt{2}\right)^{2}}{4^{2}}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(\sqrt{6}-\sqrt{2}\right)^{2} a leathnú.

$$\frac{\left(\sqrt{6}\right)^{2}-2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4^{2}}$$

Is é 6 uimhir chearnach \sqrt{6}.

$$\frac{6-2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4^{2}}$$

Fachtóirigh 6=2\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2}\sqrt{3}.

$$\frac{6-2\sqrt{2}\sqrt{3}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{4^{2}}$$

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

$$\frac{6-2\times 2\sqrt{3}+\left(\sqrt{2}\right)^{2}}{4^{2}}$$

Méadaigh -2 agus 2 chun -4 a fháil.

$$\frac{6-4\sqrt{3}+\left(\sqrt{2}\right)^{2}}{4^{2}}$$

Is é 2 uimhir chearnach \sqrt{2}.

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

Suimigh 6 agus 2 chun 8 a fháil.

$$\frac{8-4\sqrt{3}}{4^{2}}$$

Ríomh cumhacht 4 de 2 agus faigh 16.

$$\frac{8-4\sqrt{3}}{16}$$

Fachtóirigh

$$\frac{2 - \sqrt{3}}{4} = 0.0669872981077807$$