Whakaoti i te 1000/sqrt{frac{500{72}+2500/2017div2}}

$$\frac{ 1000 }{ \sqrt{ \frac{ 500 }{ 72 } + \frac{ 2500 }{ 2017 \div 2 } } }$$

Aromātai

$$\frac{120\sqrt{55205290}}{2737}\approx 325.759280011$$

Ngā Upane Otinga

Whakahekea te hautanga \frac{500}{72} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{1000}{\sqrt{\frac{125}{18}+\frac{2500}{\frac{2017}{2}}}}$$

Whakawehe 2500 ki te \frac{2017}{2} mā te whakarea 2500 ki te tau huripoki o \frac{2017}{2}.

$$\frac{1000}{\sqrt{\frac{125}{18}+2500\times \frac{2}{2017}}}$$

Tuhia te 2500\times \frac{2}{2017} hei hautanga kotahi.

$$\frac{1000}{\sqrt{\frac{125}{18}+\frac{2500\times 2}{2017}}}$$

Whakareatia te 2500 ki te 2, ka 5000.

$$\frac{1000}{\sqrt{\frac{125}{18}+\frac{5000}{2017}}}$$

Ko te maha noa iti rawa atu o 18 me 2017 ko 36306. Me tahuri \frac{125}{18} me \frac{5000}{2017} ki te hautau me te tautūnga 36306.

$$\frac{1000}{\sqrt{\frac{252125}{36306}+\frac{90000}{36306}}}$$

Tā te mea he rite te tauraro o \frac{252125}{36306} me \frac{90000}{36306}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1000}{\sqrt{\frac{252125+90000}{36306}}}$$

Tāpirihia te 252125 ki te 90000, ka 342125.

$$\frac{1000}{\sqrt{\frac{342125}{36306}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{342125}{36306}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{342125}}{\sqrt{36306}}.

$$\frac{1000}{\frac{\sqrt{342125}}{\sqrt{36306}}}$$

Tauwehea te 342125=5^{2}\times 13685. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 13685} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{13685}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{1000}{\frac{5\sqrt{13685}}{\sqrt{36306}}}$$

Tauwehea te 36306=3^{2}\times 4034. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 4034} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{4034}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{1000}{\frac{5\sqrt{13685}}{3\sqrt{4034}}}$$

Whakangāwaritia te tauraro o \frac{5\sqrt{13685}}{3\sqrt{4034}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{4034}.

$$\frac{1000}{\frac{5\sqrt{13685}\sqrt{4034}}{3\left(\sqrt{4034}\right)^{2}}}$$

Ko te pūrua o \sqrt{4034} ko 4034.

$$\frac{1000}{\frac{5\sqrt{13685}\sqrt{4034}}{3\times 4034}}$$

Hei whakarea \sqrt{13685} me \sqrt{4034}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{1000}{\frac{5\sqrt{55205290}}{3\times 4034}}$$

Whakareatia te 3 ki te 4034, ka 12102.

$$\frac{1000}{\frac{5\sqrt{55205290}}{12102}}$$

Whakawehe 1000 ki te \frac{5\sqrt{55205290}}{12102} mā te whakarea 1000 ki te tau huripoki o \frac{5\sqrt{55205290}}{12102}.

$$\frac{1000\times 12102}{5\sqrt{55205290}}$$

Me whakakore tahi te 5 i te taurunga me te tauraro.

$$\frac{200\times 12102}{\sqrt{55205290}}$$

Whakangāwaritia te tauraro o \frac{200\times 12102}{\sqrt{55205290}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{55205290}.

$$\frac{200\times 12102\sqrt{55205290}}{\left(\sqrt{55205290}\right)^{2}}$$

Ko te pūrua o \sqrt{55205290} ko 55205290.

$$\frac{200\times 12102\sqrt{55205290}}{55205290}$$

Whakareatia te 200 ki te 12102, ka 2420400.

$$\frac{2420400\sqrt{55205290}}{55205290}$$

Whakawehea te 2420400\sqrt{55205290} ki te 55205290, kia riro ko \frac{120}{2737}\sqrt{55205290}.

$$\frac{120}{2737}\sqrt{55205290}$$