Whakaoti i te sqrt{{left(9/2right)}^2+6^2}+sqrt{{left(9/2right)}^2-129/2+4}

$$\sqrt{ { \left( \frac{ 9 }{ 2 } \right) }^{ 2 } + { 6 }^{ 2 } } + \sqrt{ { \left( \frac{ 9 }{ 2 } \right) }^{ 2 } -12 \frac{ 9 }{ 2 } +4 }$$

Aromātai

$$\frac{\sqrt{31}+15}{2}\approx 10.283882181$$

Ngā Upane Otinga

Tātaihia te \frac{9}{2} mā te pū o 2, kia riro ko \frac{81}{4}.

$$\sqrt{\frac{81}{4}+6^{2}}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$\sqrt{\frac{81}{4}+36}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

Me tahuri te 36 ki te hautau \frac{144}{4}.

$$\sqrt{\frac{81}{4}+\frac{144}{4}}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

Tā te mea he rite te tauraro o \frac{81}{4} me \frac{144}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\sqrt{\frac{81+144}{4}}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

Tāpirihia te 81 ki te 144, ka 225.

$$\sqrt{\frac{225}{4}}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

Tuhia anō te pūtake rua o te whakawehenga \frac{225}{4} hei whakawehenga o ngā pūtake rua \frac{\sqrt{225}}{\sqrt{4}}. Tuhia te pūtakerua o te taurunga me te tauraro.

$$\frac{15}{2}+\sqrt{\left(\frac{9}{2}\right)^{2}-\frac{12\times 2+9}{2}+4}$$

Tātaihia te \frac{9}{2} mā te pū o 2, kia riro ko \frac{81}{4}.

$$\frac{15}{2}+\sqrt{\frac{81}{4}-\frac{12\times 2+9}{2}+4}$$

Whakareatia te 12 ki te 2, ka 24.

$$\frac{15}{2}+\sqrt{\frac{81}{4}-\frac{24+9}{2}+4}$$

Tāpirihia te 24 ki te 9, ka 33.

$$\frac{15}{2}+\sqrt{\frac{81}{4}-\frac{33}{2}+4}$$

Ko te maha noa iti rawa atu o 4 me 2 ko 4. Me tahuri \frac{81}{4} me \frac{33}{2} ki te hautau me te tautūnga 4.

$$\frac{15}{2}+\sqrt{\frac{81}{4}-\frac{66}{4}+4}$$

Tā te mea he rite te tauraro o \frac{81}{4} me \frac{66}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{15}{2}+\sqrt{\frac{81-66}{4}+4}$$

Tangohia te 66 i te 81, ka 15.

$$\frac{15}{2}+\sqrt{\frac{15}{4}+4}$$

Me tahuri te 4 ki te hautau \frac{16}{4}.

$$\frac{15}{2}+\sqrt{\frac{15}{4}+\frac{16}{4}}$$

Tā te mea he rite te tauraro o \frac{15}{4} me \frac{16}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{15}{2}+\sqrt{\frac{15+16}{4}}$$

Tāpirihia te 15 ki te 16, ka 31.

$$\frac{15}{2}+\sqrt{\frac{31}{4}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{31}{4}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{31}}{\sqrt{4}}.

$$\frac{15}{2}+\frac{\sqrt{31}}{\sqrt{4}}$$

Tātaitia te pūtakerua o 4 kia tae ki 2.

$$\frac{15}{2}+\frac{\sqrt{31}}{2}$$

Tā te mea he rite te tauraro o \frac{15}{2} me \frac{\sqrt{31}}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{15+\sqrt{31}}{2}$$

Tauwehe

$$\frac{\sqrt{31} + 15}{2} = 10.283882181415011$$