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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Immultiplika \frac{\sqrt{6}-\sqrt{2}}{4} u \frac{\sqrt{6}-\sqrt{2}}{4} biex tikseb \left(\frac{\sqrt{6}-\sqrt{2}}{4}\right)^{2}.

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

Biex tgħolli \frac{\sqrt{6}-\sqrt{2}}{4} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

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

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(\sqrt{6}-\sqrt{2}\right)^{2}.

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

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

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

Iffattura 6=2\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{3}.

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

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

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

Immultiplika -2 u 2 biex tikseb -4.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Żid 6 u 2 biex tikseb 8.

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

Ikkalkula 4 bil-power ta' 2 u tikseb 16.

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

Fattur

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