Whakaoti i te T=12432-35/frac{3774{sqrt{52}}}

$$T = \frac { 12432 - 35 } { \frac { 3774 } { \sqrt { 52 } } }$$

Whakaoti mō T

$$T = \frac{12397 \sqrt{13}}{1887} \approx 23.687344548$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 35 i te 12432, ka 12397.

$$T=\frac{12397}{\frac{3774}{\sqrt{52}}}$$

Tauwehea te 52=2^{2}\times 13. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 13} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{13}. Tuhia te pūtakerua o te 2^{2}.

$$T=\frac{12397}{\frac{3774}{2\sqrt{13}}}$$

Whakangāwaritia te tauraro o \frac{3774}{2\sqrt{13}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{13}.

$$T=\frac{12397}{\frac{3774\sqrt{13}}{2\left(\sqrt{13}\right)^{2}}}$$

Ko te pūrua o \sqrt{13} ko 13.

$$T=\frac{12397}{\frac{3774\sqrt{13}}{2\times 13}}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$T=\frac{12397}{\frac{1887\sqrt{13}}{13}}$$

Whakawehe 12397 ki te \frac{1887\sqrt{13}}{13} mā te whakarea 12397 ki te tau huripoki o \frac{1887\sqrt{13}}{13}.

$$T=\frac{12397\times 13}{1887\sqrt{13}}$$

Whakangāwaritia te tauraro o \frac{12397\times 13}{1887\sqrt{13}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{13}.

$$T=\frac{12397\times 13\sqrt{13}}{1887\left(\sqrt{13}\right)^{2}}$$

Ko te pūrua o \sqrt{13} ko 13.

$$T=\frac{12397\times 13\sqrt{13}}{1887\times 13}$$

Whakareatia te 12397 ki te 13, ka 161161.

$$T=\frac{161161\sqrt{13}}{1887\times 13}$$

Whakareatia te 1887 ki te 13, ka 24531.

$$T=\frac{161161\sqrt{13}}{24531}$$

Whakawehea te 161161\sqrt{13} ki te 24531, kia riro ko \frac{12397}{1887}\sqrt{13}.

$$T=\frac{12397}{1887}\sqrt{13}$$

Tautapa T

$$T≔\frac{12397\sqrt{13}}{1887}$$