Whakaoti i te sqrt{135}divsqrt{80}

$$\sqrt{ 135 } \div \sqrt{ 80 }$$

Aromātai

$$\frac{3\sqrt{3}}{4}\approx 1.299038106$$

Ngā Upane Otinga

Tauwehea te 135=3^{2}\times 15. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 15} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{15}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{3\sqrt{15}}{\sqrt{80}}$$

Tauwehea te 80=4^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 5} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{5}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{3\sqrt{15}}{4\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{3\sqrt{15}}{4\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{3\sqrt{15}\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{3\sqrt{15}\sqrt{5}}{4\times 5}$$

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

$$\frac{3\sqrt{5}\sqrt{3}\sqrt{5}}{4\times 5}$$

Whakareatia te \sqrt{5} ki te \sqrt{5}, ka 5.

$$\frac{3\times 5\sqrt{3}}{4\times 5}$$

Whakareatia te 4 ki te 5, ka 20.

$$\frac{3\times 5\sqrt{3}}{20}$$

Whakareatia te 3 ki te 5, ka 15.

$$\frac{15\sqrt{3}}{20}$$

Whakawehea te 15\sqrt{3} ki te 20, kia riro ko \frac{3}{4}\sqrt{3}.

$$\frac{3}{4}\sqrt{3}$$