Whakaoti i te sqrt{15}divsqrt{12}*sqrt{3/2}

$$\sqrt { 15 } \div \sqrt { 12 } \times \sqrt { \frac { 3 } { 2 } }$$

Aromātai

$$\frac{\sqrt{30}}{4}\approx 1.369306394$$

Ngā Upane Otinga

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}.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

Tauwehea te 15=3\times 5. Tuhia anō te pūtake rua o te hua \sqrt{3\times 5} hei hua o ngā pūtake rua \sqrt{3}\sqrt{5}.

$$\frac{\sqrt{3}\sqrt{5}\sqrt{3}}{2\times 3}\sqrt{\frac{3}{2}}$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$\frac{3\sqrt{5}}{2\times 3}\sqrt{\frac{3}{2}}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{3\sqrt{5}}{6}\sqrt{\frac{3}{2}}$$

Whakawehea te 3\sqrt{5} ki te 6, kia riro ko \frac{1}{2}\sqrt{5}.

$$\frac{1}{2}\sqrt{5}\sqrt{\frac{3}{2}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{3}{2}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{3}}{\sqrt{2}}.

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

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

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

Ko te pūrua o \sqrt{2} ko 2.

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

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

$$\frac{1}{2}\sqrt{5}\times \frac{\sqrt{6}}{2}$$

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

$$\frac{\sqrt{6}}{2\times 2}\sqrt{5}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\sqrt{6}}{4}\sqrt{5}$$

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

$$\frac{\sqrt{6}\sqrt{5}}{4}$$

Hei whakarea \sqrt{6} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{30}}{4}$$