Whakaoti i te (2sqrt{2/3}-5sqrt{3/8}+4sqrt{3/2})sqrt{2/3}

$$(2 \sqrt{ \frac{ 2 }{ 3 } } -5 \sqrt{ \frac{ 3 }{ 8 } } +4 \sqrt{ \frac{ 3 }{ 2 } } ) \sqrt{ \frac{ 2 }{ 3 } }$$

Aromātai

$$\frac{17}{6}\approx 2.833333333$$

Ngā Hipanga Rongoā Poto

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{2}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{2}}{\sqrt{3}}.

$$\left(2\times \frac{\sqrt{2}}{\sqrt{3}}-5\sqrt{\frac{3}{8}}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

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

$$\left(2\times \frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-5\sqrt{\frac{3}{8}}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\left(2\times \frac{\sqrt{2}\sqrt{3}}{3}-5\sqrt{\frac{3}{8}}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

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

$$\left(2\times \frac{\sqrt{6}}{3}-5\sqrt{\frac{3}{8}}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

Tuhia te 2\times \frac{\sqrt{6}}{3} hei hautanga kotahi.

$$\left(\frac{2\sqrt{6}}{3}-5\sqrt{\frac{3}{8}}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{3}{8}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{3}}{\sqrt{8}}.

$$\left(\frac{2\sqrt{6}}{3}-5\times \frac{\sqrt{3}}{\sqrt{8}}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$\left(\frac{2\sqrt{6}}{3}-5\times \frac{\sqrt{3}}{2\sqrt{2}}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

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

$$\left(\frac{2\sqrt{6}}{3}-5\times \frac{\sqrt{3}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\left(\frac{2\sqrt{6}}{3}-5\times \frac{\sqrt{3}\sqrt{2}}{2\times 2}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

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

$$\left(\frac{2\sqrt{6}}{3}-5\times \frac{\sqrt{6}}{2\times 2}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

Whakareatia te 2 ki te 2, ka 4.

$$\left(\frac{2\sqrt{6}}{3}-5\times \frac{\sqrt{6}}{4}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

Tuhia te -5\times \frac{\sqrt{6}}{4} hei hautanga kotahi.

$$\left(\frac{2\sqrt{6}}{3}+\frac{-5\sqrt{6}}{4}+4\sqrt{\frac{3}{2}}\right)\sqrt{\frac{2}{3}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{3}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{3}}{\sqrt{2}}.

$$\left(\frac{2\sqrt{6}}{3}+\frac{-5\sqrt{6}}{4}+4\times \frac{\sqrt{3}}{\sqrt{2}}\right)\sqrt{\frac{2}{3}}$$

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

$$\left(\frac{2\sqrt{6}}{3}+\frac{-5\sqrt{6}}{4}+4\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)\sqrt{\frac{2}{3}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\left(\frac{2\sqrt{6}}{3}+\frac{-5\sqrt{6}}{4}+4\times \frac{\sqrt{3}\sqrt{2}}{2}\right)\sqrt{\frac{2}{3}}$$

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

$$\left(\frac{2\sqrt{6}}{3}+\frac{-5\sqrt{6}}{4}+4\times \frac{\sqrt{6}}{2}\right)\sqrt{\frac{2}{3}}$$

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

$$\left(\frac{2\sqrt{6}}{3}+\frac{-5\sqrt{6}}{4}+2\sqrt{6}\right)\sqrt{\frac{2}{3}}$$

Pahekotia te \frac{2\sqrt{6}}{3} me 2\sqrt{6}, ka \frac{8}{3}\sqrt{6}.

$$\left(\frac{8}{3}\sqrt{6}+\frac{-5\sqrt{6}}{4}\right)\sqrt{\frac{2}{3}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{2}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{2}}{\sqrt{3}}.

$$\left(\frac{8}{3}\sqrt{6}+\frac{-5\sqrt{6}}{4}\right)\times \frac{\sqrt{2}}{\sqrt{3}}$$

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

$$\left(\frac{8}{3}\sqrt{6}+\frac{-5\sqrt{6}}{4}\right)\times \frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\left(\frac{8}{3}\sqrt{6}+\frac{-5\sqrt{6}}{4}\right)\times \frac{\sqrt{2}\sqrt{3}}{3}$$

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

$$\left(\frac{8}{3}\sqrt{6}+\frac{-5\sqrt{6}}{4}\right)\times \frac{\sqrt{6}}{3}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{8}{3}\sqrt{6}+\frac{-5\sqrt{6}}{4} ki te \frac{\sqrt{6}}{3}.

$$\frac{8}{3}\sqrt{6}\times \frac{\sqrt{6}}{3}+\frac{-5\sqrt{6}}{4}\times \frac{\sqrt{6}}{3}$$

Me whakarea te \frac{8}{3} ki te \frac{\sqrt{6}}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{8\sqrt{6}}{3\times 3}\sqrt{6}+\frac{-5\sqrt{6}}{4}\times \frac{\sqrt{6}}{3}$$

Me whakarea te \frac{-5\sqrt{6}}{4} ki te \frac{\sqrt{6}}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{8\sqrt{6}}{3\times 3}\sqrt{6}+\frac{-5\sqrt{6}\sqrt{6}}{4\times 3}$$

Whakareatia te \sqrt{6} ki te \sqrt{6}, ka 6.

$$\frac{8\sqrt{6}}{3\times 3}\sqrt{6}+\frac{-5\times 6}{4\times 3}$$

Whakareatia te 3 ki te 3, ka 9.

$$\frac{8\sqrt{6}}{9}\sqrt{6}+\frac{-5\times 6}{4\times 3}$$

Tuhia te \frac{8\sqrt{6}}{9}\sqrt{6} hei hautanga kotahi.

$$\frac{8\sqrt{6}\sqrt{6}}{9}+\frac{-5\times 6}{4\times 3}$$

Me whakakore tahi te 2\times 3 i te taurunga me te tauraro.

$$\frac{8\sqrt{6}\sqrt{6}}{9}+\frac{-5}{2}$$

Ka taea te hautanga \frac{-5}{2} te tuhi anō ko -\frac{5}{2} mā te tango i te tohu tōraro.

$$\frac{8\sqrt{6}\sqrt{6}}{9}-\frac{5}{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 9 me 2 ko 18. Whakareatia \frac{8\sqrt{6}\sqrt{6}}{9} ki te \frac{2}{2}. Whakareatia \frac{5}{2} ki te \frac{9}{9}.

$$\frac{2\times 8\sqrt{6}\sqrt{6}}{18}-\frac{5\times 9}{18}$$

Tā te mea he rite te tauraro o \frac{2\times 8\sqrt{6}\sqrt{6}}{18} me \frac{5\times 9}{18}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2\times 8\sqrt{6}\sqrt{6}-5\times 9}{18}$$

Mahia ngā whakarea i roto o 2\times 8\sqrt{6}\sqrt{6}-5\times 9.

$$\frac{96-45}{18}$$

Mahia ngā tātaitai i roto o 96-45.

$$\frac{51}{18}$$

Whakahekea te hautanga \frac{51}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{17}{6}$$

Tauwehe

$$\frac{17}{2 \cdot 3} = 2\frac{5}{6} = 2.8333333333333335$$