Whakaoti i te (2sqrt{2}-1)^2+(2sqrt{3}-1)(-2sqrt{3}-1)+frac{sqrt{12}-3}{sqrt{3}}

$$( 2 \sqrt { 2 } - 1 ) ^ { 2 } + ( 2 \sqrt { 3 } - 1 ) ( - 2 \sqrt { 3 } - 1 ) + \frac { \sqrt { 12 } - 3 } { \sqrt { 3 } }$$

Aromātai

$$-\sqrt{3}-4\sqrt{2}\approx -7.388905057$$

Ngā Hipanga Rongoā Poto

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

$$4\left(\sqrt{2}\right)^{2}-4\sqrt{2}+1+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$4\times 2-4\sqrt{2}+1+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

Whakareatia te 4 ki te 2, ka 8.

$$8-4\sqrt{2}+1+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

Tāpirihia te 8 ki te 1, ka 9.

$$9-4\sqrt{2}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\sqrt{12}-3}{\sqrt{3}}$$

Tauwehea te 12=2^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 3} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{3}. Tuhia te pūtakerua o te 2^{2}.

$$9-4\sqrt{2}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{2\sqrt{3}-3}{\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{2\sqrt{3}-3}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$9-4\sqrt{2}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$9-4\sqrt{2}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{3}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 9-4\sqrt{2} ki te \frac{3}{3}.

$$\frac{3\left(9-4\sqrt{2}\right)}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)+\frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{3}$$

Tā te mea he rite te tauraro o \frac{3\left(9-4\sqrt{2}\right)}{3} me \frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{3\left(9-4\sqrt{2}\right)+\left(2\sqrt{3}-3\right)\sqrt{3}}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

Mahia ngā whakarea i roto o 3\left(9-4\sqrt{2}\right)+\left(2\sqrt{3}-3\right)\sqrt{3}.

$$\frac{27-12\sqrt{2}+6-3\sqrt{3}}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

Mahia ngā tātaitai i roto o 27-12\sqrt{2}+6-3\sqrt{3}.

$$\frac{33-12\sqrt{2}-3\sqrt{3}}{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

Whakawehea ia wā o 33-12\sqrt{2}-3\sqrt{3} ki te 3, kia riro ko 11-4\sqrt{2}-\sqrt{3}.

$$11-4\sqrt{2}-\sqrt{3}+\left(2\sqrt{3}-1\right)\left(-2\sqrt{3}-1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2\sqrt{3}-1 ki te -2\sqrt{3}-1 ka whakakotahi i ngā kupu rite.

$$11-4\sqrt{2}-\sqrt{3}-4\left(\sqrt{3}\right)^{2}+1$$

Ko te pūrua o \sqrt{3} ko 3.

$$11-4\sqrt{2}-\sqrt{3}-4\times 3+1$$

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

$$11-4\sqrt{2}-\sqrt{3}-12+1$$

Tāpirihia te -12 ki te 1, ka -11.

$$11-4\sqrt{2}-\sqrt{3}-11$$

Tangohia te 11 i te 11, ka 0.

$$-4\sqrt{2}-\sqrt{3}$$