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

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

Aromātai

$$62-20\sqrt{6}\approx 13.010205144$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(5\sqrt{2}-2\sqrt{3}\right)^{2}.

$$25\left(\sqrt{2}\right)^{2}-20\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$25\times 2-20\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

Whakareatia te 25 ki te 2, ka 50.

$$50-20\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

Hei whakarea \sqrt{2} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$50-20\sqrt{6}+4\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$50-20\sqrt{6}+4\times 3$$

Whakareatia te 4 ki te 3, ka 12.

$$50-20\sqrt{6}+12$$

Tāpirihia te 50 ki te 12, ka 62.

$$62-20\sqrt{6}$$

Whakaroha

$$62-20\sqrt{6}$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(5\sqrt{2}-2\sqrt{3}\right)^{2}.

$$25\left(\sqrt{2}\right)^{2}-20\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$25\times 2-20\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

Whakareatia te 25 ki te 2, ka 50.

$$50-20\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}$$

Hei whakarea \sqrt{2} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$50-20\sqrt{6}+4\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$50-20\sqrt{6}+4\times 3$$

Whakareatia te 4 ki te 3, ka 12.

$$50-20\sqrt{6}+12$$

Tāpirihia te 50 ki te 12, ka 62.

$$62-20\sqrt{6}$$