Whakaoti i te sqrt{35}divsqrt{13/5}

$$\sqrt { 35 } \div \sqrt { 1 \frac { 3 } { 5 } }$$

Aromātai

$$\frac{5\sqrt{14}}{4}\approx 4.677071733$$

Ngā Upane Otinga

Whakareatia te 1 ki te 5, ka 5.

$$\frac{\sqrt{35}}{\sqrt{\frac{5+3}{5}}}$$

Tāpirihia te 5 ki te 3, ka 8.

$$\frac{\sqrt{35}}{\sqrt{\frac{8}{5}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{8}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{\sqrt{35}}{\frac{\sqrt{8}}{\sqrt{5}}}$$

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}.

$$\frac{\sqrt{35}}{\frac{2\sqrt{2}}{\sqrt{5}}}$$

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

$$\frac{\sqrt{35}}{\frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{\sqrt{35}}{\frac{2\sqrt{2}\sqrt{5}}{5}}$$

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

$$\frac{\sqrt{35}}{\frac{2\sqrt{10}}{5}}$$

Whakawehe \sqrt{35} ki te \frac{2\sqrt{10}}{5} mā te whakarea \sqrt{35} ki te tau huripoki o \frac{2\sqrt{10}}{5}.

$$\frac{\sqrt{35}\times 5}{2\sqrt{10}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{35}\times 5}{2\sqrt{10}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{10}.

$$\frac{\sqrt{35}\times 5\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

Ko te pūrua o \sqrt{10} ko 10.

$$\frac{\sqrt{35}\times 5\sqrt{10}}{2\times 10}$$

Hei whakarea \sqrt{35} me \sqrt{10}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{350}\times 5}{2\times 10}$$

Whakareatia te 2 ki te 10, ka 20.

$$\frac{\sqrt{350}\times 5}{20}$$

Tauwehea te 350=5^{2}\times 14. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 14} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{14}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{5\sqrt{14}\times 5}{20}$$

Whakareatia te 5 ki te 5, ka 25.

$$\frac{25\sqrt{14}}{20}$$

Whakawehea te 25\sqrt{14} ki te 20, kia riro ko \frac{5}{4}\sqrt{14}.

$$\frac{5}{4}\sqrt{14}$$