Whakaoti i te 22/7*75/2*sqrt{6850/4}

$$\frac{ 22 }{ 7 } \times \frac{ 75 }{ 2 } \times \sqrt{ \frac{ 6850 }{ 4 } }$$

Aromātai

$$\frac{4125\sqrt{274}}{14}\approx 4877.207114189$$

Ngā Upane Otinga

Me whakarea te \frac{22}{7} ki te \frac{75}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{22\times 75}{7\times 2}\sqrt{\frac{6850}{4}}$$

Mahia ngā whakarea i roto i te hautanga \frac{22\times 75}{7\times 2}.

$$\frac{1650}{14}\sqrt{\frac{6850}{4}}$$

Whakahekea te hautanga \frac{1650}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{825}{7}\sqrt{\frac{6850}{4}}$$

Whakahekea te hautanga \frac{6850}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{825}{7}\sqrt{\frac{3425}{2}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{3425}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{3425}}{\sqrt{2}}.

$$\frac{825}{7}\times \frac{\sqrt{3425}}{\sqrt{2}}$$

Tauwehea te 3425=5^{2}\times 137. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 137} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{137}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{825}{7}\times \frac{5\sqrt{137}}{\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{5\sqrt{137}}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{825}{7}\times \frac{5\sqrt{137}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{825}{7}\times \frac{5\sqrt{137}\sqrt{2}}{2}$$

Hei whakarea \sqrt{137} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{825}{7}\times \frac{5\sqrt{274}}{2}$$

Me whakarea te \frac{825}{7} ki te \frac{5\sqrt{274}}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{825\times 5\sqrt{274}}{7\times 2}$$

Whakareatia te 825 ki te 5, ka 4125.

$$\frac{4125\sqrt{274}}{7\times 2}$$

Whakareatia te 7 ki te 2, ka 14.

$$\frac{4125\sqrt{274}}{14}$$