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

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

Aromātai

$$55-34\sqrt{2}\approx 6.916738879$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(5\sqrt{2}-4\right)^{2}.

$$25\left(\sqrt{2}\right)^{2}-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$25\times 2-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Whakareatia te 25 ki te 2, ka 50.

$$50-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Tāpirihia te 50 ki te 16, ka 66.

$$66-40\sqrt{2}-\left(3-\sqrt{2}\right)^{2}$$

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

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+2\right)$$

Tāpirihia te 9 ki te 2, ka 11.

$$66-40\sqrt{2}-\left(11-6\sqrt{2}\right)$$

Hei kimi i te tauaro o 11-6\sqrt{2}, kimihia te tauaro o ia taurangi.

$$66-40\sqrt{2}-11+6\sqrt{2}$$

Tangohia te 11 i te 66, ka 55.

$$55-40\sqrt{2}+6\sqrt{2}$$

Pahekotia te -40\sqrt{2} me 6\sqrt{2}, ka -34\sqrt{2}.

$$55-34\sqrt{2}$$

Whakaroha

$$55-34\sqrt{2}$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(5\sqrt{2}-4\right)^{2}.

$$25\left(\sqrt{2}\right)^{2}-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$25\times 2-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Whakareatia te 25 ki te 2, ka 50.

$$50-40\sqrt{2}+16-\left(3-\sqrt{2}\right)^{2}$$

Tāpirihia te 50 ki te 16, ka 66.

$$66-40\sqrt{2}-\left(3-\sqrt{2}\right)^{2}$$

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

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Ko te pūrua o \sqrt{2} ko 2.

$$66-40\sqrt{2}-\left(9-6\sqrt{2}+2\right)$$

Tāpirihia te 9 ki te 2, ka 11.

$$66-40\sqrt{2}-\left(11-6\sqrt{2}\right)$$

Hei kimi i te tauaro o 11-6\sqrt{2}, kimihia te tauaro o ia taurangi.

$$66-40\sqrt{2}-11+6\sqrt{2}$$

Tangohia te 11 i te 66, ka 55.

$$55-40\sqrt{2}+6\sqrt{2}$$

Pahekotia te -40\sqrt{2} me 6\sqrt{2}, ka -34\sqrt{2}.

$$55-34\sqrt{2}$$