Whakaoti i te sqrt{14}divsqrt{6}*sqrt{27/2}

$$\sqrt { 14 } \div \sqrt { 6 } \times \sqrt { \frac { 27 } { 2 } }$$

Aromātai

$$\frac{3\sqrt{14}}{2}\approx 5.61248608$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{\sqrt{14}}{\sqrt{6}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{6}.

$$\frac{\sqrt{14}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}\sqrt{\frac{27}{2}}$$

Ko te pūrua o \sqrt{6} ko 6.

$$\frac{\sqrt{14}\sqrt{6}}{6}\sqrt{\frac{27}{2}}$$

Hei whakarea \sqrt{14} me \sqrt{6}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{84}}{6}\sqrt{\frac{27}{2}}$$

Tauwehea te 84=2^{2}\times 21. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 21} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{21}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{2\sqrt{21}}{6}\sqrt{\frac{27}{2}}$$

Whakawehea te 2\sqrt{21} ki te 6, kia riro ko \frac{1}{3}\sqrt{21}.

$$\frac{1}{3}\sqrt{21}\sqrt{\frac{27}{2}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{27}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{27}}{\sqrt{2}}.

$$\frac{1}{3}\sqrt{21}\times \frac{\sqrt{27}}{\sqrt{2}}$$

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

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

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

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

Ko te pūrua o \sqrt{2} ko 2.

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

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

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

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

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

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$\frac{\sqrt{6}}{2}\sqrt{21}$$

Tuhia te \frac{\sqrt{6}}{2}\sqrt{21} hei hautanga kotahi.

$$\frac{\sqrt{6}\sqrt{21}}{2}$$

Hei whakarea \sqrt{6} me \sqrt{21}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{126}}{2}$$

Tauwehea te 126=3^{2}\times 14. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 14} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{14}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{3\sqrt{14}}{2}$$