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

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

Arvuta

$$\frac{3\sqrt{13046875000000008517}}{125000000000000}\approx 0,000086689$$

Lahenduse etapid

Taandage 2 ja 2.

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

Korrutage 408 ja 16, et leida 6528.

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

Arvutage -19 aste 10 ja leidke \frac{1}{10000000000000000000}.

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

Korrutage 6528 ja \frac{1}{10000000000000000000}, et leida \frac{51}{78125000000000000}.

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

Liitke 1 ja \frac{51}{78125000000000000}, et leida \frac{78125000000000051}{78125000000000000}.

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

Korrutage 2 ja 167, et leida 334.

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

Arvutage -27 aste 10 ja leidke \frac{1}{1000000000000000000000000000}.

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

Korrutage 334 ja \frac{1}{1000000000000000000000000000}, et leida \frac{167}{500000000000000000000000000}.

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

Arvutage 8 aste 10 ja leidke 100000000.

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

Korrutage 3 ja 100000000, et leida 300000000.

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

Arvutage 2 aste 300000000 ja leidke 90000000000000000.

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

Korrutage \frac{167}{500000000000000000000000000} ja 90000000000000000, et leida \frac{1503}{50000000000}.

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

Jagage \frac{78125000000000051}{78125000000000000} väärtusega \frac{1503}{50000000000}, korrutades \frac{78125000000000051}{78125000000000000} väärtuse \frac{1503}{50000000000} pöördväärtusega.

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

Korrutage \frac{78125000000000051}{78125000000000000} ja \frac{50000000000}{1503}, et leida \frac{78125000000000051}{2348437500}.

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

Kirjutage: allüksus \sqrt{\frac{78125000000000051}{2348437500}}: allüksus juured \frac{\sqrt{78125000000000051}}{\sqrt{2348437500}}.

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

Tegurda 2348437500=3750^{2}\times 167. Kirjutage \sqrt{3750^{2}\times 167} toote juured, kui see ruut \sqrt{3750^{2}}\sqrt{167}. Leidke 3750^{2} ruutjuur.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{167} nimetaja \frac{\sqrt{78125000000000051}}{3750\sqrt{167}} nimetaja.

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

\sqrt{167} ruut on 167.

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

\sqrt{78125000000000051} ja \sqrt{167} korrutage numbrid, mis on sama juur.

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

Korrutage 3750 ja 167, et leida 626250.

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

Arvutage -27 aste 10 ja leidke \frac{1}{1000000000000000000000000000}.

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

Korrutage 167 ja \frac{1}{1000000000000000000000000000}, et leida \frac{167}{1000000000000000000000000000}.

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

Arvutage 8 aste 10 ja leidke 100000000.

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

Korrutage 3 ja 100000000, et leida 300000000.

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

Arvutage 2 aste 300000000 ja leidke 90000000000000000.

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

Korrutage \frac{167}{1000000000000000000000000000} ja 90000000000000000, et leida \frac{1503}{100000000000}.

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

Korrutage omavahel \frac{1503}{100000000000} ja \frac{\sqrt{13046875000000008517}}{626250}. Seejärel taandage murd võimaluse korral vähimale ühiskordsele.

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

Taandage 501 nii lugejas kui ka nimetajas.

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

Korrutage 1250 ja 100000000000, et leida 125000000000000.

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