Whakaoti i te (3-sqrt{5}-4-sqrt{2})^2

$$( 3 - \sqrt { 5 } - 4 - \sqrt { 2 } ) ^ { 2 }$$

Aromātai

$$2\left(\sqrt{2}+\sqrt{5}+\sqrt{10}+4\right)\approx 21.6251184$$

Ngā Upane Otinga

Tangohia te 4 i te 3, ka -1.

$$\left(-1-\sqrt{5}-\sqrt{2}\right)^{2}$$

Pūrua -1-\sqrt{5}-\sqrt{2}.

$$2\sqrt{2}\sqrt{5}+\left(\sqrt{2}\right)^{2}+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$2\sqrt{10}+\left(\sqrt{2}\right)^{2}+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1$$

Ko te pūrua o \sqrt{2} ko 2.

$$2\sqrt{10}+2+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1$$

Ko te pūrua o \sqrt{5} ko 5.

$$2\sqrt{10}+2+5+2\sqrt{2}+2\sqrt{5}+1$$

Tāpirihia te 2 ki te 5, ka 7.

$$2\sqrt{10}+7+2\sqrt{2}+2\sqrt{5}+1$$

Tāpirihia te 7 ki te 1, ka 8.

$$2\sqrt{10}+8+2\sqrt{2}+2\sqrt{5}$$

Whakaroha

$$2 \sqrt{2} + 2 \sqrt{5} + 2 \sqrt{10} + 8 = 21.6251184$$

Ngā Upane Otinga

Tangohia te 4 i te 3, ka -1.

$$\left(-1-\sqrt{5}-\sqrt{2}\right)^{2}$$

Pūrua -1-\sqrt{5}-\sqrt{2}.

$$2\sqrt{2}\sqrt{5}+\left(\sqrt{2}\right)^{2}+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$2\sqrt{10}+\left(\sqrt{2}\right)^{2}+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1$$

Ko te pūrua o \sqrt{2} ko 2.

$$2\sqrt{10}+2+\left(\sqrt{5}\right)^{2}+2\sqrt{2}+2\sqrt{5}+1$$

Ko te pūrua o \sqrt{5} ko 5.

$$2\sqrt{10}+2+5+2\sqrt{2}+2\sqrt{5}+1$$

Tāpirihia te 2 ki te 5, ka 7.

$$2\sqrt{10}+7+2\sqrt{2}+2\sqrt{5}+1$$

Tāpirihia te 7 ki te 1, ka 8.

$$2\sqrt{10}+8+2\sqrt{2}+2\sqrt{5}$$