Whakaoti i te frac{4sqrt{3}}{2-sqrt{2}}-30/4sqrt{3-sqrt{18}}-frac{sqrt{18}}{3-sqrt{12}}

$$\frac { 4 \sqrt { 3 } } { 2 - \sqrt { 2 } } - \frac { 30 } { 4 \sqrt { 3 } - \sqrt { 18 } } - \frac { \sqrt { 18 } } { 3 - \sqrt { 12 } }$$

Aromātai

$$4\sqrt{6}\approx 9.797958971$$

Ngā Hipanga Rongoā Poto

Whakangāwaritia te tauraro o \frac{4\sqrt{3}}{2-\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te 2+\sqrt{2}.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{\left(2-\sqrt{2}\right)\left(2+\sqrt{2}\right)}-\frac{30}{4\sqrt{3}-\sqrt{18}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Whakaarohia te \left(2-\sqrt{2}\right)\left(2+\sqrt{2}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2^{2}-\left(\sqrt{2}\right)^{2}}-\frac{30}{4\sqrt{3}-\sqrt{18}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Pūrua 2. Pūrua \sqrt{2}.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{4-2}-\frac{30}{4\sqrt{3}-\sqrt{18}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Tangohia te 2 i te 4, ka 2.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30}{4\sqrt{3}-\sqrt{18}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30}{4\sqrt{3}-3\sqrt{2}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Whakangāwaritia te tauraro o \frac{30}{4\sqrt{3}-3\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te 4\sqrt{3}+3\sqrt{2}.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{\left(4\sqrt{3}-3\sqrt{2}\right)\left(4\sqrt{3}+3\sqrt{2}\right)}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Whakaarohia te \left(4\sqrt{3}-3\sqrt{2}\right)\left(4\sqrt{3}+3\sqrt{2}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{\left(4\sqrt{3}\right)^{2}-\left(-3\sqrt{2}\right)^{2}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Whakarohaina te \left(4\sqrt{3}\right)^{2}.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{4^{2}\left(\sqrt{3}\right)^{2}-\left(-3\sqrt{2}\right)^{2}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{16\left(\sqrt{3}\right)^{2}-\left(-3\sqrt{2}\right)^{2}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{16\times 3-\left(-3\sqrt{2}\right)^{2}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Whakareatia te 16 ki te 3, ka 48.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{48-\left(-3\sqrt{2}\right)^{2}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Whakarohaina te \left(-3\sqrt{2}\right)^{2}.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{48-\left(-3\right)^{2}\left(\sqrt{2}\right)^{2}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Tātaihia te -3 mā te pū o 2, kia riro ko 9.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{48-9\left(\sqrt{2}\right)^{2}}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{48-9\times 2}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Whakareatia te 9 ki te 2, ka 18.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{48-18}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Tangohia te 18 i te 48, ka 30.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{30}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Me whakakore te 30 me te 30.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-\left(4\sqrt{3}+3\sqrt{2}\right)-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Hei kimi i te tauaro o 4\sqrt{3}+3\sqrt{2}, kimihia te tauaro o ia taurangi.

$$\frac{4\sqrt{3}\left(2+\sqrt{2}\right)}{2}-4\sqrt{3}-3\sqrt{2}-\frac{\sqrt{18}}{3-\sqrt{12}}$$

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

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

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}.

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

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

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

Whakaarohia te \left(3-2\sqrt{3}\right)\left(3+2\sqrt{3}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

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

Whakarohaina te \left(-2\sqrt{3}\right)^{2}.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

Whakareatia te 4 ki te 3, ka 12.

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

Tangohia te 12 i te 9, ka -3.

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

Me whakakore te -3 me te -3.

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

Ko te tauaro o -\sqrt{2}\left(3+2\sqrt{3}\right) ko \sqrt{2}\left(3+2\sqrt{3}\right).

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

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

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

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

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

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

$$\frac{8\sqrt{3}+4\sqrt{6}-8\sqrt{3}-6\sqrt{2}}{2}+\sqrt{2}\left(3+2\sqrt{3}\right)$$

Mahia ngā tātaitai i roto o 8\sqrt{3}+4\sqrt{6}-8\sqrt{3}-6\sqrt{2}.

$$\frac{4\sqrt{6}-6\sqrt{2}}{2}+\sqrt{2}\left(3+2\sqrt{3}\right)$$

Whakawehea ia wā o 4\sqrt{6}-6\sqrt{2} ki te 2, kia riro ko 2\sqrt{6}-3\sqrt{2}.

$$2\sqrt{6}-3\sqrt{2}+\sqrt{2}\left(3+2\sqrt{3}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt{2} ki te 3+2\sqrt{3}.

$$2\sqrt{6}-3\sqrt{2}+3\sqrt{2}+2\sqrt{2}\sqrt{3}$$

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

$$2\sqrt{6}-3\sqrt{2}+3\sqrt{2}+2\sqrt{6}$$

Pahekotia te -3\sqrt{2} me 3\sqrt{2}, ka 0.

$$2\sqrt{6}+2\sqrt{6}$$

Pahekotia te 2\sqrt{6} me 2\sqrt{6}, ka 4\sqrt{6}.

$$4\sqrt{6}$$