Whakaoti i te sqrt{13.5div4/3div3.14}

$$\sqrt{ 13.5 \div \frac{ 4 }{ 3 } \div 3.14 }$$

Aromātai

$$\frac{45\sqrt{157}}{314}\approx 1.79569549$$

Ngā Upane Otinga

Tuhia te \frac{\frac{13.5}{\frac{4}{3}}}{3.14} hei hautanga kotahi.

$$\sqrt{\frac{13.5}{\frac{4}{3}\times 3.14}}$$

Me tahuri ki tau ā-ira 3.14 ki te hautau \frac{314}{100}. Whakahekea te hautanga \frac{314}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{\frac{13.5}{\frac{4}{3}\times \frac{157}{50}}}$$

Me whakarea te \frac{4}{3} ki te \frac{157}{50} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{13.5}{\frac{4\times 157}{3\times 50}}}$$

Mahia ngā whakarea i roto i te hautanga \frac{4\times 157}{3\times 50}.

$$\sqrt{\frac{13.5}{\frac{628}{150}}}$$

Whakahekea te hautanga \frac{628}{150} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{\frac{13.5}{\frac{314}{75}}}$$

Whakawehe 13.5 ki te \frac{314}{75} mā te whakarea 13.5 ki te tau huripoki o \frac{314}{75}.

$$\sqrt{13.5\times \frac{75}{314}}$$

Me tahuri ki tau ā-ira 13.5 ki te hautau \frac{135}{10}. Whakahekea te hautanga \frac{135}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\sqrt{\frac{27}{2}\times \frac{75}{314}}$$

Me whakarea te \frac{27}{2} ki te \frac{75}{314} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\sqrt{\frac{27\times 75}{2\times 314}}$$

Mahia ngā whakarea i roto i te hautanga \frac{27\times 75}{2\times 314}.

$$\sqrt{\frac{2025}{628}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{2025}{628}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{2025}}{\sqrt{628}}.

$$\frac{\sqrt{2025}}{\sqrt{628}}$$

Tātaitia te pūtakerua o 2025 kia tae ki 45.

$$\frac{45}{\sqrt{628}}$$

Tauwehea te 628=2^{2}\times 157. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 157} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{157}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{45}{2\sqrt{157}}$$

Whakangāwaritia te tauraro o \frac{45}{2\sqrt{157}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{157}.

$$\frac{45\sqrt{157}}{2\left(\sqrt{157}\right)^{2}}$$

Ko te pūrua o \sqrt{157} ko 157.

$$\frac{45\sqrt{157}}{2\times 157}$$

Whakareatia te 2 ki te 157, ka 314.

$$\frac{45\sqrt{157}}{314}$$