Whakaoti i te 85.3-78.2/sqrt{frac{6.5{8}+6.3/8}}

$$\frac{ 85.3-78.2 }{ \sqrt{ \frac{ 6.5 }{ 8 } + \frac{ 6.3 }{ 8 } } }$$

Aromātai

$$\frac{71\sqrt{10}}{40}\approx 5.613042847$$

Ngā Upane Otinga

Tangohia te 78.2 i te 85.3, ka 7.1.

$$\frac{7.1}{\sqrt{\frac{6.5}{8}+\frac{6.3}{8}}}$$

Whakarohaina te \frac{6.5}{8} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\frac{7.1}{\sqrt{\frac{65}{80}+\frac{6.3}{8}}}$$

Whakahekea te hautanga \frac{65}{80} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{7.1}{\sqrt{\frac{13}{16}+\frac{6.3}{8}}}$$

Whakarohaina te \frac{6.3}{8} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\frac{7.1}{\sqrt{\frac{13}{16}+\frac{63}{80}}}$$

Ko te maha noa iti rawa atu o 16 me 80 ko 80. Me tahuri \frac{13}{16} me \frac{63}{80} ki te hautau me te tautūnga 80.

$$\frac{7.1}{\sqrt{\frac{65}{80}+\frac{63}{80}}}$$

Tā te mea he rite te tauraro o \frac{65}{80} me \frac{63}{80}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7.1}{\sqrt{\frac{65+63}{80}}}$$

Tāpirihia te 65 ki te 63, ka 128.

$$\frac{7.1}{\sqrt{\frac{128}{80}}}$$

Whakahekea te hautanga \frac{128}{80} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 16.

$$\frac{7.1}{\sqrt{\frac{8}{5}}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{8}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{7.1}{\frac{\sqrt{8}}{\sqrt{5}}}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{7.1}{\frac{2\sqrt{2}}{\sqrt{5}}}$$

Whakangāwaritia te tauraro o \frac{2\sqrt{2}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{7.1}{\frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{7.1}{\frac{2\sqrt{2}\sqrt{5}}{5}}$$

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{7.1}{\frac{2\sqrt{10}}{5}}$$

Whakawehe 7.1 ki te \frac{2\sqrt{10}}{5} mā te whakarea 7.1 ki te tau huripoki o \frac{2\sqrt{10}}{5}.

$$\frac{7.1\times 5}{2\sqrt{10}}$$

Whakangāwaritia te tauraro o \frac{7.1\times 5}{2\sqrt{10}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{10}.

$$\frac{7.1\times 5\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

Ko te pūrua o \sqrt{10} ko 10.

$$\frac{7.1\times 5\sqrt{10}}{2\times 10}$$

Whakareatia te 7.1 ki te 5, ka 35.5.

$$\frac{35.5\sqrt{10}}{2\times 10}$$

Whakareatia te 2 ki te 10, ka 20.

$$\frac{35.5\sqrt{10}}{20}$$

Whakawehea te 35.5\sqrt{10} ki te 20, kia riro ko 1.775\sqrt{10}.

$$1.775\sqrt{10}$$