Whakaoti i te [10-(sqrt{7}-sqrt{3})^2]

$$[ 10 - ( \sqrt { 7 } - \sqrt { 3 } ) ^ { 2 } ]$$

Aromātai

$$2\sqrt{21}\approx 9.16515139$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{7}-\sqrt{3}\right)^{2}.

$$10-\left(\left(\sqrt{7}\right)^{2}-2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)$$

Ko te pūrua o \sqrt{7} ko 7.

$$10-\left(7-2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)$$

Hei whakarea \sqrt{7} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$10-\left(7-2\sqrt{21}+\left(\sqrt{3}\right)^{2}\right)$$

Ko te pūrua o \sqrt{3} ko 3.

$$10-\left(7-2\sqrt{21}+3\right)$$

Tāpirihia te 7 ki te 3, ka 10.

$$10-\left(10-2\sqrt{21}\right)$$

Hei kimi i te tauaro o 10-2\sqrt{21}, kimihia te tauaro o ia taurangi.

$$10-10+2\sqrt{21}$$

Tangohia te 10 i te 10, ka 0.

$$2\sqrt{21}$$

Whakaroha

$$2 \sqrt{21} = 9.16515139$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{7}-\sqrt{3}\right)^{2}.

$$10-\left(\left(\sqrt{7}\right)^{2}-2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)$$

Ko te pūrua o \sqrt{7} ko 7.

$$10-\left(7-2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)$$

Hei whakarea \sqrt{7} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$10-\left(7-2\sqrt{21}+\left(\sqrt{3}\right)^{2}\right)$$

Ko te pūrua o \sqrt{3} ko 3.

$$10-\left(7-2\sqrt{21}+3\right)$$

Tāpirihia te 7 ki te 3, ka 10.

$$10-\left(10-2\sqrt{21}\right)$$

Hei kimi i te tauaro o 10-2\sqrt{21}, kimihia te tauaro o ia taurangi.

$$10-10+2\sqrt{21}$$

Tangohia te 10 i te 10, ka 0.

$$2\sqrt{21}$$