Whakaoti i te 3sqrt{22/3}div1/2sqrt{2/5}-1/8sqrt{15}

$$3 \sqrt{ 2 \frac{ 2 }{ 3 } } \div \frac{ 1 }{ 2 } \sqrt{ \frac{ 2 }{ 5 } } - \frac{ 1 }{ 8 } \sqrt{ 15 }$$

Aromātai

$$\frac{59\sqrt{15}}{40}\approx 5.712650436$$

Ngā Upane Otinga

Whakareatia te 2 ki te 3, ka 6.

$$\frac{3\sqrt{\frac{6+2}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Tāpirihia te 6 ki te 2, ka 8.

$$\frac{3\sqrt{\frac{8}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

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

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

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}.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

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

$$\frac{3\times \frac{2\sqrt{6}}{3}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Me whakakore te 3 me te 3.

$$\frac{2\sqrt{6}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Whakawehe 2\sqrt{6} ki te \frac{1}{2} mā te whakarea 2\sqrt{6} ki te tau huripoki o \frac{1}{2}.

$$2\sqrt{6}\times 2\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Whakareatia te 2 ki te 2, ka 4.

$$4\sqrt{6}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{2}}{\sqrt{5}}-\frac{1}{8}\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{1}{8}\sqrt{15}$$

Ko te pūrua o \sqrt{5} ko 5.

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{5}-\frac{1}{8}\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{10}}{5}-\frac{1}{8}\sqrt{15}$$

Tuhia te 4\times \frac{\sqrt{10}}{5} hei hautanga kotahi.

$$\frac{4\sqrt{10}}{5}\sqrt{6}-\frac{1}{8}\sqrt{15}$$

Tuhia te \frac{4\sqrt{10}}{5}\sqrt{6} hei hautanga kotahi.

$$\frac{4\sqrt{10}\sqrt{6}}{5}-\frac{1}{8}\sqrt{15}$$

Hei whakarea \sqrt{10} me \sqrt{6}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{4\sqrt{60}}{5}-\frac{1}{8}\sqrt{15}$$

Tauwehea te 60=2^{2}\times 15. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 15} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{15}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{4\times 2\sqrt{15}}{5}-\frac{1}{8}\sqrt{15}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{8\sqrt{15}}{5}-\frac{1}{8}\sqrt{15}$$

Pahekotia te \frac{8\sqrt{15}}{5} me -\frac{1}{8}\sqrt{15}, ka \frac{59}{40}\sqrt{15}.

$$\frac{59}{40}\sqrt{15}$$