Whakaoti i te sqrt{87/12-(1/12)^2*10}

$$\sqrt { \frac { 87 } { 12 } - ( 1 / 12 ) ^ { 2 } \times 10 }$$

Aromātai

$$\frac{\sqrt{1034}}{12}\approx 2.679655865$$

Ngā Upane Otinga

Whakahekea te hautanga \frac{87}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\sqrt{\frac{29}{4}-\left(\frac{1}{12}\right)^{2}\times 10}$$

Tātaihia te \frac{1}{12} mā te pū o 2, kia riro ko \frac{1}{144}.

$$\sqrt{\frac{29}{4}-\frac{1}{144}\times 10}$$

Whakareatia te \frac{1}{144} ki te 10, ka \frac{10}{144}.

$$\sqrt{\frac{29}{4}-\frac{10}{144}}$$

Whakahekea te hautanga \frac{10}{144} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{\frac{29}{4}-\frac{5}{72}}$$

Ko te maha noa iti rawa atu o 4 me 72 ko 72. Me tahuri \frac{29}{4} me \frac{5}{72} ki te hautau me te tautūnga 72.

$$\sqrt{\frac{522}{72}-\frac{5}{72}}$$

Tā te mea he rite te tauraro o \frac{522}{72} me \frac{5}{72}, me tango rāua mā te tango i ō raua taurunga.

$$\sqrt{\frac{522-5}{72}}$$

Tangohia te 5 i te 522, ka 517.

$$\sqrt{\frac{517}{72}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{517}{72}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{517}}{\sqrt{72}}.

$$\frac{\sqrt{517}}{\sqrt{72}}$$

Tauwehea te 72=6^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{6^{2}\times 2} hei hua o ngā pūtake rua \sqrt{6^{2}}\sqrt{2}. Tuhia te pūtakerua o te 6^{2}.

$$\frac{\sqrt{517}}{6\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{517}}{6\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{\sqrt{517}\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\sqrt{517}\sqrt{2}}{6\times 2}$$

Hei whakarea \sqrt{517} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{1034}}{6\times 2}$$

Whakareatia te 6 ki te 2, ka 12.

$$\frac{\sqrt{1034}}{12}$$