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

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

Aromātai

$$\frac{7\sqrt{3}}{3}\approx 4.041451884$$

Ngā Hipanga Rongoā Poto

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}.

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

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}.

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

Me whakakore te 3 me te 3.

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

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

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

Tātaitia te pūtakerua o 4 kia tae ki 2.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

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

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

Tātaitia te pūtakerua o 1 kia tae ki 1.

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

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

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

Ko te pūrua o \sqrt{2} ko 2.

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

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

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

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

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

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

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

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

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

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

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

Tā te mea he rite te tauraro o \frac{3\left(3\sqrt{3}-2\sqrt{2}\right)}{3} me \frac{2\sqrt{3}-6\sqrt{2}}{3}, me tango rāua mā te tango i ō raua taurunga.

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

Mahia ngā whakarea i roto o 3\left(3\sqrt{3}-2\sqrt{2}\right)-\left(2\sqrt{3}-6\sqrt{2}\right).

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

Mahia ngā tātaitai i roto o 9\sqrt{3}-6\sqrt{2}-2\sqrt{3}+6\sqrt{2}.

$$\frac{7\sqrt{3}}{3}$$