Whakaoti i te sqrt{frac{left(396-3998right)^2+left(398-3998right)^2+left(395-3998right)^2+left(403-3998right)^2+{left(399-3998right)}^{2}+{left(403-3998right)}^{2}+{left(402-3998right)}^2+{left(399-3998right)}^2+{left(404-3998right)}^2+{left(399+3998right)}^2}{90}}

$$\sqrt{ \frac{ { \left(396-3998 \right) }^{ 2 } + { \left(398-3998 \right) }^{ 2 } + { \left(395-3998 \right) }^{ 2 } + { \left(403-3998 \right) }^{ 2 } + { \left(399-3998 \right) }^{ 2 } + { \left(403-3998 \right) }^{ 2 } + { \left(402-3998 \right) }^{ 2 } + { \left(399-3998 \right) }^{ 2 } + { \left(404-3998 \right) }^{ 2 } + { \left(399+3998 \right) }^{ 2 } }{ 90 } }$$

Aromātai

$$\frac{13\sqrt{2009635}}{15}\approx 1228.600495596$$

Ngā Upane Otinga

Tangohia te 3998 i te 396, ka -3602.

$$\sqrt{\frac{\left(-3602\right)^{2}+\left(398-3998\right)^{2}+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tātaihia te -3602 mā te pū o 2, kia riro ko 12974404.

$$\sqrt{\frac{12974404+\left(398-3998\right)^{2}+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tangohia te 3998 i te 398, ka -3600.

$$\sqrt{\frac{12974404+\left(-3600\right)^{2}+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tātaihia te -3600 mā te pū o 2, kia riro ko 12960000.

$$\sqrt{\frac{12974404+12960000+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tāpirihia te 12974404 ki te 12960000, ka 25934404.

$$\sqrt{\frac{25934404+\left(395-3998\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tangohia te 3998 i te 395, ka -3603.

$$\sqrt{\frac{25934404+\left(-3603\right)^{2}+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tātaihia te -3603 mā te pū o 2, kia riro ko 12981609.

$$\sqrt{\frac{25934404+12981609+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tāpirihia te 25934404 ki te 12981609, ka 38916013.

$$\sqrt{\frac{38916013+\left(403-3998\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tangohia te 3998 i te 403, ka -3595.

$$\sqrt{\frac{38916013+\left(-3595\right)^{2}+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tātaihia te -3595 mā te pū o 2, kia riro ko 12924025.

$$\sqrt{\frac{38916013+12924025+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tāpirihia te 38916013 ki te 12924025, ka 51840038.

$$\sqrt{\frac{51840038+\left(399-3998\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tangohia te 3998 i te 399, ka -3599.

$$\sqrt{\frac{51840038+\left(-3599\right)^{2}+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tātaihia te -3599 mā te pū o 2, kia riro ko 12952801.

$$\sqrt{\frac{51840038+12952801+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tāpirihia te 51840038 ki te 12952801, ka 64792839.

$$\sqrt{\frac{64792839+\left(403-3998\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tangohia te 3998 i te 403, ka -3595.

$$\sqrt{\frac{64792839+\left(-3595\right)^{2}+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tātaihia te -3595 mā te pū o 2, kia riro ko 12924025.

$$\sqrt{\frac{64792839+12924025+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tāpirihia te 64792839 ki te 12924025, ka 77716864.

$$\sqrt{\frac{77716864+\left(402-3998\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tangohia te 3998 i te 402, ka -3596.

$$\sqrt{\frac{77716864+\left(-3596\right)^{2}+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tātaihia te -3596 mā te pū o 2, kia riro ko 12931216.

$$\sqrt{\frac{77716864+12931216+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tāpirihia te 77716864 ki te 12931216, ka 90648080.

$$\sqrt{\frac{90648080+\left(399-3998\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tangohia te 3998 i te 399, ka -3599.

$$\sqrt{\frac{90648080+\left(-3599\right)^{2}+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tātaihia te -3599 mā te pū o 2, kia riro ko 12952801.

$$\sqrt{\frac{90648080+12952801+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tāpirihia te 90648080 ki te 12952801, ka 103600881.

$$\sqrt{\frac{103600881+\left(404-3998\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tangohia te 3998 i te 404, ka -3594.

$$\sqrt{\frac{103600881+\left(-3594\right)^{2}+\left(399+3998\right)^{2}}{90}}$$

Tātaihia te -3594 mā te pū o 2, kia riro ko 12916836.

$$\sqrt{\frac{103600881+12916836+\left(399+3998\right)^{2}}{90}}$$

Tāpirihia te 103600881 ki te 12916836, ka 116517717.

$$\sqrt{\frac{116517717+\left(399+3998\right)^{2}}{90}}$$

Tāpirihia te 399 ki te 3998, ka 4397.

$$\sqrt{\frac{116517717+4397^{2}}{90}}$$

Tātaihia te 4397 mā te pū o 2, kia riro ko 19333609.

$$\sqrt{\frac{116517717+19333609}{90}}$$

Tāpirihia te 116517717 ki te 19333609, ka 135851326.

$$\sqrt{\frac{135851326}{90}}$$

Whakahekea te hautanga \frac{135851326}{90} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\sqrt{\frac{67925663}{45}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{67925663}{45}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{67925663}}{\sqrt{45}}.

$$\frac{\sqrt{67925663}}{\sqrt{45}}$$

Tauwehea te 67925663=13^{2}\times 401927. Tuhia anō te pūtake rua o te hua \sqrt{13^{2}\times 401927} hei hua o ngā pūtake rua \sqrt{13^{2}}\sqrt{401927}. Tuhia te pūtakerua o te 13^{2}.

$$\frac{13\sqrt{401927}}{\sqrt{45}}$$

Tauwehea te 45=3^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 5} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{5}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{13\sqrt{401927}}{3\sqrt{5}}$$

Whakangāwaritia te tauraro o \frac{13\sqrt{401927}}{3\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

$$\frac{13\sqrt{401927}\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}$$

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{13\sqrt{401927}\sqrt{5}}{3\times 5}$$

Hei whakarea \sqrt{401927} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{13\sqrt{2009635}}{3\times 5}$$

Whakareatia te 3 ki te 5, ka 15.

$$\frac{13\sqrt{2009635}}{15}$$