Whakaoti i te sqrt{75+(45^2+40)/65*10^4}

$$\sqrt { \frac { 75 + ( 45 ^ { 2 } + 40 ) } { 65 \times 10 ^ { 4 } } }$$

Aromātai

$$\frac{\sqrt{1391}}{650}\approx 0.057378634$$

Ngā Upane Otinga

Tātaihia te 45 mā te pū o 2, kia riro ko 2025.

$$\sqrt{\frac{75+2025+40}{65\times 10^{4}}}$$

Tāpirihia te 75 ki te 2025, ka 2100.

$$\sqrt{\frac{2100+40}{65\times 10^{4}}}$$

Tāpirihia te 2100 ki te 40, ka 2140.

$$\sqrt{\frac{2140}{65\times 10^{4}}}$$

Tātaihia te 10 mā te pū o 4, kia riro ko 10000.

$$\sqrt{\frac{2140}{65\times 10000}}$$

Whakareatia te 65 ki te 10000, ka 650000.

$$\sqrt{\frac{2140}{650000}}$$

Whakahekea te hautanga \frac{2140}{650000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$\sqrt{\frac{107}{32500}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{107}{32500}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{107}}{\sqrt{32500}}.

$$\frac{\sqrt{107}}{\sqrt{32500}}$$

Tauwehea te 32500=50^{2}\times 13. Tuhia anō te pūtake rua o te hua \sqrt{50^{2}\times 13} hei hua o ngā pūtake rua \sqrt{50^{2}}\sqrt{13}. Tuhia te pūtakerua o te 50^{2}.

$$\frac{\sqrt{107}}{50\sqrt{13}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{107}}{50\sqrt{13}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{13}.

$$\frac{\sqrt{107}\sqrt{13}}{50\left(\sqrt{13}\right)^{2}}$$

Ko te pūrua o \sqrt{13} ko 13.

$$\frac{\sqrt{107}\sqrt{13}}{50\times 13}$$

Hei whakarea \sqrt{107} me \sqrt{13}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{1391}}{50\times 13}$$

Whakareatia te 50 ki te 13, ka 650.

$$\frac{\sqrt{1391}}{650}$$