Whakaoti i te (7+sqrt{3})(2-sqrt{3})^2+(2^2-3)+sqrt{3}

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

Aromātai

$$38-20\sqrt{3}\approx 3.358983849$$

Ngā Upane Otinga

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

$$\left(7+\sqrt{3}\right)\left(4-4\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)+2^{2}-3+\sqrt{3}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\left(7+\sqrt{3}\right)\left(4-4\sqrt{3}+3\right)+2^{2}-3+\sqrt{3}$$

Tāpirihia te 4 ki te 3, ka 7.

$$\left(7+\sqrt{3}\right)\left(7-4\sqrt{3}\right)+2^{2}-3+\sqrt{3}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 7+\sqrt{3} ki te 7-4\sqrt{3} ka whakakotahi i ngā kupu rite.

$$49-21\sqrt{3}-4\left(\sqrt{3}\right)^{2}+2^{2}-3+\sqrt{3}$$

Ko te pūrua o \sqrt{3} ko 3.

$$49-21\sqrt{3}-4\times 3+2^{2}-3+\sqrt{3}$$

Whakareatia te -4 ki te 3, ka -12.

$$49-21\sqrt{3}-12+2^{2}-3+\sqrt{3}$$

Tangohia te 12 i te 49, ka 37.

$$37-21\sqrt{3}+2^{2}-3+\sqrt{3}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$37-21\sqrt{3}+4-3+\sqrt{3}$$

Tāpirihia te 37 ki te 4, ka 41.

$$41-21\sqrt{3}-3+\sqrt{3}$$

Tangohia te 3 i te 41, ka 38.

$$38-21\sqrt{3}+\sqrt{3}$$

Pahekotia te -21\sqrt{3} me \sqrt{3}, ka -20\sqrt{3}.

$$38-20\sqrt{3}$$