Whakaoti i te (1/sqrt{2}*8sqrt{2}*2/3)*1/2

$$( \frac { 1 } { \sqrt { 2 } } \times 8 \sqrt { 2 } \times \frac { 2 } { 3 } ) \times \frac { 1 } { 2 }$$

Aromātai

$$\frac{8}{3}\approx 2.666666667$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{1}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$8\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sqrt{2}\times \frac{2}{3}\times \frac{1}{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$8\times \frac{\sqrt{2}}{2}\sqrt{2}\times \frac{2}{3}\times \frac{1}{2}$$

Tuhia te 8\times \frac{2}{3} hei hautanga kotahi.

$$\frac{8\times 2}{3}\times \frac{\sqrt{2}}{2}\sqrt{2}\times \frac{1}{2}$$

Whakareatia te 8 ki te 2, ka 16.

$$\frac{16}{3}\times \frac{\sqrt{2}}{2}\sqrt{2}\times \frac{1}{2}$$

Me whakarea te \frac{16}{3} ki te \frac{1}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{16\times 1}{3\times 2}\times \frac{\sqrt{2}}{2}\sqrt{2}$$

Mahia ngā whakarea i roto i te hautanga \frac{16\times 1}{3\times 2}.

$$\frac{16}{6}\times \frac{\sqrt{2}}{2}\sqrt{2}$$

Whakahekea te hautanga \frac{16}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{8}{3}\times \frac{\sqrt{2}}{2}\sqrt{2}$$

Me whakarea te \frac{8}{3} ki te \frac{\sqrt{2}}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{8\sqrt{2}}{3\times 2}\sqrt{2}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\frac{4\sqrt{2}}{3}\sqrt{2}$$

Tuhia te \frac{4\sqrt{2}}{3}\sqrt{2} hei hautanga kotahi.

$$\frac{4\sqrt{2}\sqrt{2}}{3}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$\frac{4\times 2}{3}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{8}{3}$$

Tauwehe

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$