Whakaoti i te 258(sqrt{65*35/2000}

$$258( \sqrt{ \frac{ 65 \times 35 }{ 2000 } }$$

Aromātai

$$\frac{129\sqrt{455}}{10}\approx 275.166404199$$

Ngā Upane Otinga

Whakareatia te 65 ki te 35, ka 2275.

$$258\sqrt{\frac{2275}{2000}}$$

Whakahekea te hautanga \frac{2275}{2000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$258\sqrt{\frac{91}{80}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{91}{80}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{91}}{\sqrt{80}}.

$$258\times \frac{\sqrt{91}}{\sqrt{80}}$$

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}.

$$258\times \frac{\sqrt{91}}{4\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{91}}{4\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$258\times \frac{\sqrt{91}\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$258\times \frac{\sqrt{91}\sqrt{5}}{4\times 5}$$

Hei whakarea \sqrt{91} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$258\times \frac{\sqrt{455}}{4\times 5}$$

Whakareatia te 4 ki te 5, ka 20.

$$258\times \frac{\sqrt{455}}{20}$$

Tuhia te 258\times \frac{\sqrt{455}}{20} hei hautanga kotahi.

$$\frac{258\sqrt{455}}{20}$$

Whakawehea te 258\sqrt{455} ki te 20, kia riro ko \frac{129}{10}\sqrt{455}.

$$\frac{129}{10}\sqrt{455}$$