Whakaoti i te 2sqrt{1/27}-2/3sqrt{18}-sqrt{4/3}-4sqrt{1/2}

$$2 \sqrt{ \frac{ 1 }{ 27 } } - \frac{ 2 }{ 3 } \sqrt{ 18 } - \sqrt{ \frac{ 4 }{ 3 } } -4 \sqrt{ \frac{ 1 }{ 2 } }$$

Aromātai

$$-\frac{4\sqrt{3}}{9}-4\sqrt{2}\approx -6.426654608$$

Ngā Hipanga Rongoā Poto

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{27}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{27}}.

$$2\times \frac{\sqrt{1}}{\sqrt{27}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$2\times \frac{1}{\sqrt{27}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

$$2\times \frac{1}{3\sqrt{3}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Whakangāwaritia te tauraro o \frac{1}{3\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$2\times \frac{\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$2\times \frac{\sqrt{3}}{3\times 3}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Whakareatia te 3 ki te 3, ka 9.

$$2\times \frac{\sqrt{3}}{9}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Tuhia te 2\times \frac{\sqrt{3}}{9} hei hautanga kotahi.

$$\frac{2\sqrt{3}}{9}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

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}.

$$\frac{2\sqrt{3}}{9}-\frac{2}{3}\times 3\sqrt{2}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Me whakakore te 3 me te 3.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{4}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{4}}{\sqrt{3}}.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{\sqrt{4}}{\sqrt{3}}-4\sqrt{\frac{1}{2}}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2}{\sqrt{3}}-4\sqrt{\frac{1}{2}}$$

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

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

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\sqrt{\frac{1}{2}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\times \frac{\sqrt{1}}{\sqrt{2}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\times \frac{1}{\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

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

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\times \frac{\sqrt{2}}{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 4 me te 2.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-2\sqrt{2}$$

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

$$\frac{2\sqrt{3}}{9}-4\sqrt{2}-\frac{2\sqrt{3}}{3}$$

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

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

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

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

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

$$\frac{2\sqrt{3}-36\sqrt{2}}{9}-\frac{2\sqrt{3}}{3}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 9 me 3 ko 9. Whakareatia \frac{2\sqrt{3}}{3} ki te \frac{3}{3}.

$$\frac{2\sqrt{3}-36\sqrt{2}}{9}-\frac{3\times 2\sqrt{3}}{9}$$

Tā te mea he rite te tauraro o \frac{2\sqrt{3}-36\sqrt{2}}{9} me \frac{3\times 2\sqrt{3}}{9}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2\sqrt{3}-36\sqrt{2}-3\times 2\sqrt{3}}{9}$$

Mahia ngā whakarea i roto o 2\sqrt{3}-36\sqrt{2}-3\times 2\sqrt{3}.

$$\frac{2\sqrt{3}-36\sqrt{2}-6\sqrt{3}}{9}$$

Mahia ngā tātaitai i roto o 2\sqrt{3}-36\sqrt{2}-6\sqrt{3}.

$$\frac{-4\sqrt{3}-36\sqrt{2}}{9}$$

Tauwehe

$$\frac{4 {(-\sqrt{3} - 9 \sqrt{2})}}{9} = -6.426654608411882$$