Whakaoti i te {left(1+sqrt{3}right)}^2+{left(frac{sqrt{3}}{3}+1right)}^2=

$${ \left(1+ \sqrt{ 3 } \right) }^{ 2 } + { \left( \frac{ \sqrt{ 3 } }{ 3 } +1 \right) }^{ 2 } =$$

Aromātai

$$\frac{8\left(\sqrt{3}+2\right)}{3}\approx 9.952135487$$

Ngā Hipanga Rongoā Poto

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(1+\sqrt{3}\right)^{2}.

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

Ko te pūrua o \sqrt{3} ko 3.

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

Tāpirihia te 1 ki te 3, ka 4.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}}{3}+1\right)^{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{3}{3}.

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

Tā te mea he rite te tauraro o \frac{\sqrt{3}}{3} me \frac{3}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Kia whakarewa i te \frac{\sqrt{3}+3}{3} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 4+2\sqrt{3} ki te \frac{3^{2}}{3^{2}}.

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

Tā te mea he rite te tauraro o \frac{\left(4+2\sqrt{3}\right)\times 3^{2}}{3^{2}} me \frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Mahia ngā whakarea i roto o \left(4+2\sqrt{3}\right)\times 3^{2}+\left(\sqrt{3}+3\right)^{2}.

$$\frac{36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9}{3^{2}}$$

Mahia ngā tātaitai i roto o 36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9.

$$\frac{48+24\sqrt{3}}{3^{2}}$$

Whakarohaina te 3^{2}.

$$\frac{48+24\sqrt{3}}{9}$$

Whakaroha

$$\frac{8 \sqrt{3} + 16}{3} = 9.95213548685034$$

Ngā Hipanga Rongoā Poto

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(1+\sqrt{3}\right)^{2}.

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

Ko te pūrua o \sqrt{3} ko 3.

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

Tāpirihia te 1 ki te 3, ka 4.

$$4+2\sqrt{3}+\left(\frac{\sqrt{3}}{3}+1\right)^{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 1 ki te \frac{3}{3}.

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

Tā te mea he rite te tauraro o \frac{\sqrt{3}}{3} me \frac{3}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Kia whakarewa i te \frac{\sqrt{3}+3}{3} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 4+2\sqrt{3} ki te \frac{3^{2}}{3^{2}}.

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

Tā te mea he rite te tauraro o \frac{\left(4+2\sqrt{3}\right)\times 3^{2}}{3^{2}} me \frac{\left(\sqrt{3}+3\right)^{2}}{3^{2}}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Mahia ngā whakarea i roto o \left(4+2\sqrt{3}\right)\times 3^{2}+\left(\sqrt{3}+3\right)^{2}.

$$\frac{36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9}{3^{2}}$$

Mahia ngā tātaitai i roto o 36+18\sqrt{3}+\left(\sqrt{3}\right)^{2}+6\sqrt{3}+9.

$$\frac{48+24\sqrt{3}}{3^{2}}$$

Whakarohaina te 3^{2}.

$$\frac{48+24\sqrt{3}}{9}$$