Whakaoti i te 2/3sqrt{20}*(1/3sqrt{48})divsqrt{22/3}

$$\frac { 2 } { 3 } \sqrt { 20 } \times ( \frac { 1 } { 3 } \sqrt { 48 } ) \div \sqrt { 2 \frac { 2 } { 3 } }$$

Aromātai

$$\frac{4\sqrt{10}}{3}\approx 4.216370214$$

Ngā Upane Otinga

Tauwehea te 20=2^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 5} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{5}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{\frac{2}{3}\times 2\sqrt{5}\times \frac{1}{3}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

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

$$\frac{\frac{2\times 2}{3}\sqrt{5}\times \frac{1}{3}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\frac{4}{3}\sqrt{5}\times \frac{1}{3}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Me whakarea te \frac{4}{3} ki te \frac{1}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{4\times 1}{3\times 3}\sqrt{5}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Mahia ngā whakarea i roto i te hautanga \frac{4\times 1}{3\times 3}.

$$\frac{\frac{4}{9}\sqrt{5}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Tauwehea te 48=4^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 3} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{3}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{\frac{4}{9}\sqrt{5}\times 4\sqrt{3}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Tuhia te \frac{4}{9}\times 4 hei hautanga kotahi.

$$\frac{\frac{4\times 4}{9}\sqrt{5}\sqrt{3}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Whakareatia te 4 ki te 4, ka 16.

$$\frac{\frac{16}{9}\sqrt{5}\sqrt{3}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Hei whakarea \sqrt{5} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\frac{16}{9}\sqrt{15}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{\frac{16}{9}\sqrt{15}}{\sqrt{\frac{6+2}{3}}}$$

Tāpirihia te 6 ki te 2, ka 8.

$$\frac{\frac{16}{9}\sqrt{15}}{\sqrt{\frac{8}{3}}}$$

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

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{\sqrt{8}}{\sqrt{3}}}$$

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}.

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{2}}{\sqrt{3}}}$$

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

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{2}\sqrt{3}}{3}}$$

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

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{6}}{3}}$$

Whakawehe \frac{16}{9}\sqrt{15} ki te \frac{2\sqrt{6}}{3} mā te whakarea \frac{16}{9}\sqrt{15} ki te tau huripoki o \frac{2\sqrt{6}}{3}.

$$\frac{\frac{16}{9}\sqrt{15}\times 3}{2\sqrt{6}}$$

Whakangāwaritia te tauraro o \frac{\frac{16}{9}\sqrt{15}\times 3}{2\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$\frac{\frac{16}{9}\sqrt{15}\times 3\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{\frac{16}{9}\sqrt{15}\times 3\sqrt{6}}{2\times 6}$$

Tuhia te \frac{16}{9}\times 3 hei hautanga kotahi.

$$\frac{\frac{16\times 3}{9}\sqrt{15}\sqrt{6}}{2\times 6}$$

Whakareatia te 16 ki te 3, ka 48.

$$\frac{\frac{48}{9}\sqrt{15}\sqrt{6}}{2\times 6}$$

Whakahekea te hautanga \frac{48}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{\frac{16}{3}\sqrt{15}\sqrt{6}}{2\times 6}$$

Hei whakarea \sqrt{15} me \sqrt{6}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\frac{16}{3}\sqrt{90}}{2\times 6}$$

Whakareatia te 2 ki te 6, ka 12.

$$\frac{\frac{16}{3}\sqrt{90}}{12}$$

Tauwehea te 90=3^{2}\times 10. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 10} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{10}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{\frac{16}{3}\times 3\sqrt{10}}{12}$$

Me whakakore te 3 me te 3.

$$\frac{16\sqrt{10}}{12}$$

Whakawehea te 16\sqrt{10} ki te 12, kia riro ko \frac{4}{3}\sqrt{10}.

$$\frac{4}{3}\sqrt{10}$$