Whakaoti i te sqrt{frac{1+408*1610^-19/2*16710^-27left(310^8right)^2}2*167{10}^-27{left(3{10}^8right)}^2}{2}

$$\frac{ \sqrt{ \frac{ 1+408 \cdot 16 { 10 }^{ -19 } }{ 2 \cdot 167 { 10 }^{ -27 } { \left(3 { 10 }^{ 8 } \right) }^{ 2 } } } 2 \cdot 167 { 10 }^{ -27 } { \left(3 { 10 }^{ 8 } \right) }^{ 2 } }{ 2 }$$

Aromātai

$$\frac{3\sqrt{13046875000000008517}}{125000000000000}\approx 0.000086689$$

Ngā Upane Otinga

Me whakakore te 2 me te 2.

$$167\sqrt{\frac{1+408\times 16\times 10^{-19}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakareatia te 408 ki te 16, ka 6528.

$$167\sqrt{\frac{1+6528\times 10^{-19}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Tātaihia te 10 mā te pū o -19, kia riro ko \frac{1}{10000000000000000000}.

$$167\sqrt{\frac{1+6528\times \frac{1}{10000000000000000000}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakareatia te 6528 ki te \frac{1}{10000000000000000000}, ka \frac{51}{78125000000000000}.

$$167\sqrt{\frac{1+\frac{51}{78125000000000000}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Tāpirihia te 1 ki te \frac{51}{78125000000000000}, ka \frac{78125000000000051}{78125000000000000}.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{2\times 167\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakareatia te 2 ki te 167, ka 334.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{334\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Tātaihia te 10 mā te pū o -27, kia riro ko \frac{1}{1000000000000000000000000000}.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{334\times \frac{1}{1000000000000000000000000000}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakareatia te 334 ki te \frac{1}{1000000000000000000000000000}, ka \frac{167}{500000000000000000000000000}.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{167}{500000000000000000000000000}\times \left(3\times 10^{8}\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Tātaihia te 10 mā te pū o 8, kia riro ko 100000000.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{167}{500000000000000000000000000}\times \left(3\times 100000000\right)^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakareatia te 3 ki te 100000000, ka 300000000.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{167}{500000000000000000000000000}\times 300000000^{2}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Tātaihia te 300000000 mā te pū o 2, kia riro ko 90000000000000000.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{167}{500000000000000000000000000}\times 90000000000000000}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakareatia te \frac{167}{500000000000000000000000000} ki te 90000000000000000, ka \frac{1503}{50000000000}.

$$167\sqrt{\frac{\frac{78125000000000051}{78125000000000000}}{\frac{1503}{50000000000}}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakawehe \frac{78125000000000051}{78125000000000000} ki te \frac{1503}{50000000000} mā te whakarea \frac{78125000000000051}{78125000000000000} ki te tau huripoki o \frac{1503}{50000000000}.

$$167\sqrt{\frac{78125000000000051}{78125000000000000}\times \frac{50000000000}{1503}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakareatia te \frac{78125000000000051}{78125000000000000} ki te \frac{50000000000}{1503}, ka \frac{78125000000000051}{2348437500}.

$$167\sqrt{\frac{78125000000000051}{2348437500}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{78125000000000051}{2348437500}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{78125000000000051}}{\sqrt{2348437500}}.

$$167\times \frac{\sqrt{78125000000000051}}{\sqrt{2348437500}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Tauwehea te 2348437500=3750^{2}\times 167. Tuhia anō te pūtake rua o te hua \sqrt{3750^{2}\times 167} hei hua o ngā pūtake rua \sqrt{3750^{2}}\sqrt{167}. Tuhia te pūtakerua o te 3750^{2}.

$$167\times \frac{\sqrt{78125000000000051}}{3750\sqrt{167}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakangāwaritia te tauraro o \frac{\sqrt{78125000000000051}}{3750\sqrt{167}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{167}.

$$167\times \frac{\sqrt{78125000000000051}\sqrt{167}}{3750\left(\sqrt{167}\right)^{2}}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Ko te pūrua o \sqrt{167} ko 167.

$$167\times \frac{\sqrt{78125000000000051}\sqrt{167}}{3750\times 167}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Hei whakarea \sqrt{78125000000000051} me \sqrt{167}, whakareatia ngā tau i raro i te pūtake rua.

$$167\times \frac{\sqrt{13046875000000008517}}{3750\times 167}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Whakareatia te 3750 ki te 167, ka 626250.

$$167\times \frac{\sqrt{13046875000000008517}}{626250}\times 10^{-27}\times \left(3\times 10^{8}\right)^{2}$$

Tātaihia te 10 mā te pū o -27, kia riro ko \frac{1}{1000000000000000000000000000}.

$$167\times \frac{\sqrt{13046875000000008517}}{626250}\times \frac{1}{1000000000000000000000000000}\times \left(3\times 10^{8}\right)^{2}$$

Whakareatia te 167 ki te \frac{1}{1000000000000000000000000000}, ka \frac{167}{1000000000000000000000000000}.

$$\frac{167}{1000000000000000000000000000}\times \frac{\sqrt{13046875000000008517}}{626250}\times \left(3\times 10^{8}\right)^{2}$$

Tātaihia te 10 mā te pū o 8, kia riro ko 100000000.

$$\frac{167}{1000000000000000000000000000}\times \frac{\sqrt{13046875000000008517}}{626250}\times \left(3\times 100000000\right)^{2}$$

Whakareatia te 3 ki te 100000000, ka 300000000.

$$\frac{167}{1000000000000000000000000000}\times \frac{\sqrt{13046875000000008517}}{626250}\times 300000000^{2}$$

Tātaihia te 300000000 mā te pū o 2, kia riro ko 90000000000000000.

$$\frac{167}{1000000000000000000000000000}\times \frac{\sqrt{13046875000000008517}}{626250}\times 90000000000000000$$

Whakareatia te \frac{167}{1000000000000000000000000000} ki te 90000000000000000, ka \frac{1503}{100000000000}.

$$\frac{1503}{100000000000}\times \frac{\sqrt{13046875000000008517}}{626250}$$

Me whakarea te \frac{1503}{100000000000} ki te \frac{\sqrt{13046875000000008517}}{626250} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1503\sqrt{13046875000000008517}}{100000000000\times 626250}$$

Me whakakore tahi te 501 i te taurunga me te tauraro.

$$\frac{3\sqrt{13046875000000008517}}{1250\times 100000000000}$$

Whakareatia te 1250 ki te 100000000000, ka 125000000000000.

$$\frac{3\sqrt{13046875000000008517}}{125000000000000}$$