Whakaoti i te 3sqrt{22/3}+1/2sqrt{2/5}*(-1/8sqrt{15})

$$3 \sqrt { 2 \frac { 2 } { 3 } } + \frac { 1 } { 2 } \sqrt { \frac { 2 } { 5 } } \times ( - \frac { 1 } { 8 } \sqrt { 15 } )$$

Aromātai

$$\frac{31\sqrt{6}}{16}\approx 4.745886377$$

Ngā Hipanga Rongoā Poto

Whakareatia te 2 ki te 3, ka 6.

$$3\sqrt{\frac{6+2}{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Tāpirihia te 6 ki te 2, ka 8.

$$3\sqrt{\frac{8}{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$3\times \frac{\sqrt{8}}{\sqrt{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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}.

$$3\times \frac{2\sqrt{2}}{\sqrt{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$3\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Ko te pūrua o \sqrt{3} ko 3.

$$3\times \frac{2\sqrt{2}\sqrt{3}}{3}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$3\times \frac{2\sqrt{6}}{3}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Me whakakore te 3 me te 3.

$$2\sqrt{6}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{2}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{2}}{\sqrt{5}}.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{2}}{\sqrt{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Whakangāwaritia te tauraro o \frac{\sqrt{2}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Ko te pūrua o \sqrt{5} ko 5.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{2}\sqrt{5}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Me whakarea te \frac{1}{2} ki te -\frac{1}{8} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$2\sqrt{6}+\frac{1\left(-1\right)}{2\times 8}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\left(-1\right)}{2\times 8}.

$$2\sqrt{6}+\frac{-1}{16}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Ka taea te hautanga \frac{-1}{16} te tuhi anō ko -\frac{1}{16} mā te tango i te tohu tōraro.

$$2\sqrt{6}-\frac{1}{16}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Me whakarea te -\frac{1}{16} ki te \frac{\sqrt{10}}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$2\sqrt{6}+\frac{-\sqrt{10}}{16\times 5}\sqrt{15}$$

Tuhia te \frac{-\sqrt{10}}{16\times 5}\sqrt{15} hei hautanga kotahi.

$$2\sqrt{6}+\frac{-\sqrt{10}\sqrt{15}}{16\times 5}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 2\sqrt{6} ki te \frac{16\times 5}{16\times 5}.

$$\frac{2\sqrt{6}\times 16\times 5}{16\times 5}+\frac{-\sqrt{10}\sqrt{15}}{16\times 5}$$

Tā te mea he rite te tauraro o \frac{2\sqrt{6}\times 16\times 5}{16\times 5} me \frac{-\sqrt{10}\sqrt{15}}{16\times 5}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2\sqrt{6}\times 16\times 5-\sqrt{10}\sqrt{15}}{16\times 5}$$

Mahia ngā whakarea i roto o 2\sqrt{6}\times 16\times 5-\sqrt{10}\sqrt{15}.

$$\frac{160\sqrt{6}-5\sqrt{6}}{16\times 5}$$

Mahia ngā tātaitai i roto o 160\sqrt{6}-5\sqrt{6}.

$$\frac{155\sqrt{6}}{16\times 5}$$

Me whakakore tahi te 5 i te taurunga me te tauraro.

$$\frac{31\sqrt{6}}{16}$$