Whakaoti i te sqrt{31/5}divsqrt{15/5}

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

Aromātai

$$\frac{2\sqrt{10}}{5}\approx 1.264911064$$

Ngā Upane Otinga

Whakareatia te 3 ki te 5, ka 15.

$$\frac{\sqrt{\frac{15+1}{5}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

Tāpirihia te 15 ki te 1, ka 16.

$$\frac{\sqrt{\frac{16}{5}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{16}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{16}}{\sqrt{5}}.

$$\frac{\frac{\sqrt{16}}{\sqrt{5}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

Tātaitia te pūtakerua o 16 kia tae ki 4.

$$\frac{\frac{4}{\sqrt{5}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

Whakangāwaritia te tauraro o \frac{4}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{\frac{4\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{\sqrt{\frac{1\times 5+5}{5}}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{\frac{1\times 5+5}{5}}}$$

Whakareatia te 1 ki te 5, ka 5.

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

Tāpirihia te 5 ki te 5, ka 10.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{\frac{10}{5}}}$$

Whakawehea te 10 ki te 5, kia riro ko 2.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{2}}$$

Tuhia te \frac{\frac{4\sqrt{5}}{5}}{\sqrt{2}} hei hautanga kotahi.

$$\frac{4\sqrt{5}}{5\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{4\sqrt{5}}{5\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{4\sqrt{5}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{4\sqrt{5}\sqrt{2}}{5\times 2}$$

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

$$\frac{4\sqrt{10}}{5\times 2}$$

Whakareatia te 5 ki te 2, ka 10.

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

Whakawehea te 4\sqrt{10} ki te 10, kia riro ko \frac{2}{5}\sqrt{10}.

$$\frac{2}{5}\sqrt{10}$$