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

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

I-evaluate

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

Mga Hakbang ng Solution

I-cancel out ang 2 at 2.

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

I-multiply ang 408 at 16 para makuha ang 6528.

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

Kalkulahin ang 10 sa power ng -19 at kunin ang \frac{1}{10000000000000000000}.

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

I-multiply ang 6528 at \frac{1}{10000000000000000000} para makuha ang \frac{51}{78125000000000000}.

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

Idagdag ang 1 at \frac{51}{78125000000000000} para makuha ang \frac{78125000000000051}{78125000000000000}.

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

I-multiply ang 2 at 167 para makuha ang 334.

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

Kalkulahin ang 10 sa power ng -27 at kunin ang \frac{1}{1000000000000000000000000000}.

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

I-multiply ang 334 at \frac{1}{1000000000000000000000000000} para makuha ang \frac{167}{500000000000000000000000000}.

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

Kalkulahin ang 10 sa power ng 8 at kunin ang 100000000.

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

I-multiply ang 3 at 100000000 para makuha ang 300000000.

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

Kalkulahin ang 300000000 sa power ng 2 at kunin ang 90000000000000000.

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

I-multiply ang \frac{167}{500000000000000000000000000} at 90000000000000000 para makuha ang \frac{1503}{50000000000}.

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

I-divide ang \frac{78125000000000051}{78125000000000000} gamit ang \frac{1503}{50000000000} sa pamamagitan ng pagmu-multiply sa \frac{78125000000000051}{78125000000000000} gamit ang reciprocal ng \frac{1503}{50000000000}.

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

I-multiply ang \frac{78125000000000051}{78125000000000000} at \frac{50000000000}{1503} para makuha ang \frac{78125000000000051}{2348437500}.

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

I-rewrite ang square root ng division na \sqrt{\frac{78125000000000051}{2348437500}} bilang division ng mga square root na \frac{\sqrt{78125000000000051}}{\sqrt{2348437500}}.

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

I-factor out ang 2348437500=3750^{2}\times 167. I-rewrite ang square root ng product na \sqrt{3750^{2}\times 167} bilang product ng mga square root na \sqrt{3750^{2}}\sqrt{167}. Kunin ang square root ng 3750^{2}.

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

I-rationalize ang denominator ng \frac{\sqrt{78125000000000051}}{3750\sqrt{167}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{167}.

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

Ang square ng \sqrt{167} ay 167.

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

Para i-multiply ang \sqrt{78125000000000051} at \sqrt{167}, i-multiply ang mga numero sa ilalim ng square root.

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

I-multiply ang 3750 at 167 para makuha ang 626250.

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

Kalkulahin ang 10 sa power ng -27 at kunin ang \frac{1}{1000000000000000000000000000}.

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

I-multiply ang 167 at \frac{1}{1000000000000000000000000000} para makuha ang \frac{167}{1000000000000000000000000000}.

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

Kalkulahin ang 10 sa power ng 8 at kunin ang 100000000.

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

I-multiply ang 3 at 100000000 para makuha ang 300000000.

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

Kalkulahin ang 300000000 sa power ng 2 at kunin ang 90000000000000000.

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

I-multiply ang \frac{167}{1000000000000000000000000000} at 90000000000000000 para makuha ang \frac{1503}{100000000000}.

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

I-multiply ang \frac{1503}{100000000000} sa \frac{\sqrt{13046875000000008517}}{626250} sa pamamagitan ng pag-multiply ng numerator sa numerator at denominator sa denominator.

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

I-cancel out ang 501 sa parehong numerator at denominator.

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

I-multiply ang 1250 at 100000000000 para makuha ang 125000000000000.

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