Whakaoti i te (10sqrt{6}+10sqrt{2})^2

$$( 10 \sqrt { 6 } + 10 \sqrt { 2 } ) ^ { 2 }$$

Aromātai

$$400\left(\sqrt{3}+2\right)\approx 1492.820323028$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(10\sqrt{6}+10\sqrt{2}\right)^{2}.

$$100\left(\sqrt{6}\right)^{2}+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{6} ko 6.

$$100\times 6+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Whakareatia te 100 ki te 6, ka 600.

$$600+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

$$600+200\sqrt{2}\sqrt{3}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+200\times 2\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Whakareatia te 200 ki te 2, ka 400.

$$600+400\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$600+400\sqrt{3}+100\times 2$$

Whakareatia te 100 ki te 2, ka 200.

$$600+400\sqrt{3}+200$$

Tāpirihia te 600 ki te 200, ka 800.

$$800+400\sqrt{3}$$

Whakaroha

$$400 \sqrt{3} + 800 = 1492.820323028$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(10\sqrt{6}+10\sqrt{2}\right)^{2}.

$$100\left(\sqrt{6}\right)^{2}+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{6} ko 6.

$$100\times 6+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Whakareatia te 100 ki te 6, ka 600.

$$600+200\sqrt{6}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

Tauwehea te 6=2\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2\times 3} hei hua o ngā pūtake rua \sqrt{2}\sqrt{3}.

$$600+200\sqrt{2}\sqrt{3}\sqrt{2}+100\left(\sqrt{2}\right)^{2}$$

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

$$600+200\times 2\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Whakareatia te 200 ki te 2, ka 400.

$$600+400\sqrt{3}+100\left(\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$600+400\sqrt{3}+100\times 2$$

Whakareatia te 100 ki te 2, ka 200.

$$600+400\sqrt{3}+200$$

Tāpirihia te 600 ki te 200, ka 800.

$$800+400\sqrt{3}$$