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

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

Arvuta

$$-\frac{\sqrt{3}}{4}+\frac{1}{2}\approx 0,066987298$$

Lahenduse etapid

Korrutage \frac{\sqrt{6}-\sqrt{2}}{4} ja \frac{\sqrt{6}-\sqrt{2}}{4}, et leida \left(\frac{\sqrt{6}-\sqrt{2}}{4}\right)^{2}.

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

Avaldise \frac{\sqrt{6}-\sqrt{2}}{4} astendamiseks astendage nii lugeja kui ka nimetaja ning seejärel tehke jagamistehe.

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

Kasutage kaksliikme \left(\sqrt{6}-\sqrt{2}\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

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

\sqrt{6} ruut on 6.

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

Tegurda 6=2\times 3. Kirjutage \sqrt{2\times 3} toote juured, kui see ruut \sqrt{2}\sqrt{3}.

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

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

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

Korrutage -2 ja 2, et leida -4.

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

\sqrt{2} ruut on 2.

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

Liitke 6 ja 2, et leida 8.

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

Arvutage 2 aste 4 ja leidke 16.

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

Lahuta teguriteks

$$\frac{2 - \sqrt{3}}{4} = 0,0669872981077807$$