Whakaoti i te 12sqrt{1/6}div3sqrt{7/12}*1/2sqrt{101/2}

$$12 \sqrt { \frac { 1 } { 6 } } \div 3 \sqrt { \frac { 7 } { 12 } } \times \frac { 1 } { 2 } \sqrt { 10 \frac { 1 } { 2 } }$$

Aromātai

$$\frac{7\sqrt{3}}{6}\approx 2.020725942$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{6}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{6}}.

$$\frac{12\times \frac{\sqrt{1}}{\sqrt{6}}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$\frac{12\times \frac{1}{\sqrt{6}}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$\frac{12\times \frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{12\times \frac{\sqrt{6}}{6}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Whakakorea atu te tauwehe pūnoa nui rawa 6 i roto i te 12 me te 6.

$$\frac{2\sqrt{6}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{7}{12}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{7}}{\sqrt{12}}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}}{\sqrt{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Tauwehea te 12=2^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 3} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{3}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}}{2\sqrt{3}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{7}}{2\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}\sqrt{3}}{2\times 3}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Hei whakarea \sqrt{7} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{2\times 3}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

Whakareatia te 10 ki te 2, ka 20.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\sqrt{\frac{20+1}{2}}$$

Tāpirihia te 20 ki te 1, ka 21.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\sqrt{\frac{21}{2}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{21}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{21}}{\sqrt{2}}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{21}}{\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{21}}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{21}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{21}\sqrt{2}}{2}$$

Hei whakarea \sqrt{21} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{42}}{2}$$

Me whakarea te \frac{2\sqrt{6}}{3} ki te \frac{\sqrt{21}}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{2\sqrt{6}\sqrt{21}}{3\times 6}\times \frac{1}{2}\times \frac{\sqrt{42}}{2}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\frac{\sqrt{6}\sqrt{21}}{3\times 3}\times \frac{1}{2}\times \frac{\sqrt{42}}{2}$$

Me whakarea te \frac{\sqrt{6}\sqrt{21}}{3\times 3} ki te \frac{1}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\sqrt{6}\sqrt{21}}{3\times 3\times 2}\times \frac{\sqrt{42}}{2}$$

Me whakarea te \frac{\sqrt{6}\sqrt{21}}{3\times 3\times 2} ki te \frac{\sqrt{42}}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\sqrt{6}\sqrt{21}\sqrt{42}}{3\times 3\times 2\times 2}$$

Tauwehea te 42=6\times 7. Tuhia anō te pūtake rua o te hua \sqrt{6\times 7} hei hua o ngā pūtake rua \sqrt{6}\sqrt{7}.

$$\frac{\sqrt{6}\sqrt{21}\sqrt{6}\sqrt{7}}{3\times 3\times 2\times 2}$$

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

$$\frac{6\sqrt{21}\sqrt{7}}{3\times 3\times 2\times 2}$$

Tauwehea te 21=7\times 3. Tuhia anō te pūtake rua o te hua \sqrt{7\times 3} hei hua o ngā pūtake rua \sqrt{7}\sqrt{3}.

$$\frac{6\sqrt{7}\sqrt{3}\sqrt{7}}{3\times 3\times 2\times 2}$$

Whakareatia te \sqrt{7} ki te \sqrt{7}, ka 7.

$$\frac{6\times 7\sqrt{3}}{3\times 3\times 2\times 2}$$

Whakareatia te 6 ki te 7, ka 42.

$$\frac{42\sqrt{3}}{3\times 3\times 2\times 2}$$

Whakareatia te 3 ki te 3, ka 9.

$$\frac{42\sqrt{3}}{9\times 2\times 2}$$

Whakareatia te 9 ki te 2, ka 18.

$$\frac{42\sqrt{3}}{18\times 2}$$

Whakareatia te 18 ki te 2, ka 36.

$$\frac{42\sqrt{3}}{36}$$

Whakawehea te 42\sqrt{3} ki te 36, kia riro ko \frac{7}{6}\sqrt{3}.

$$\frac{7}{6}\sqrt{3}$$