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

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

Izračunaj

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

Koraci rješenja

Skraćivanje 2 i 2.

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

Pomnožite 408 i 16 da biste dobili 6528.

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

Izračunajte koliko je -19 na 10 da biste dobili \frac{1}{10000000000000000000}.

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

Pomnožite 6528 i \frac{1}{10000000000000000000} da biste dobili \frac{51}{78125000000000000}.

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

Dodajte 1 broju \frac{51}{78125000000000000} da biste dobili \frac{78125000000000051}{78125000000000000}.

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

Pomnožite 2 i 167 da biste dobili 334.

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

Izračunajte koliko je -27 na 10 da biste dobili \frac{1}{1000000000000000000000000000}.

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

Pomnožite 334 i \frac{1}{1000000000000000000000000000} da biste dobili \frac{167}{500000000000000000000000000}.

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

Izračunajte koliko je 8 na 10 da biste dobili 100000000.

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

Pomnožite 3 i 100000000 da biste dobili 300000000.

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

Izračunajte koliko je 2 na 300000000 da biste dobili 90000000000000000.

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

Pomnožite \frac{167}{500000000000000000000000000} i 90000000000000000 da biste dobili \frac{1503}{50000000000}.

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

Podijelite \frac{78125000000000051}{78125000000000000} s \frac{1503}{50000000000} tako da pomnožite \frac{78125000000000051}{78125000000000000} s brojem recipročnim broju \frac{1503}{50000000000}.

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

Pomnožite \frac{78125000000000051}{78125000000000000} i \frac{50000000000}{1503} da biste dobili \frac{78125000000000051}{2348437500}.

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

Ponovno napišite kvadratni korijen dijeljenja \sqrt{\frac{78125000000000051}{2348437500}} kao dijeljenje kvadrata korijena \frac{\sqrt{78125000000000051}}{\sqrt{2348437500}}.

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

Rastavite 2348437500=3750^{2}\times 167 na faktore. Ponovno napišite kvadratni korijen proizvoda \sqrt{3750^{2}\times 167} kao umnožak kvadrata korijena \sqrt{3750^{2}}\sqrt{167}. Izračunajte kvadratni korijen od 3750^{2}.

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

Racionalizirajte nazivnik \frac{\sqrt{78125000000000051}}{3750\sqrt{167}} množenje brojnik i nazivnik \sqrt{167}.

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

Kvadrat od \sqrt{167} je 167.

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

Da biste pomnožite \sqrt{78125000000000051} i \sqrt{167}, pomnožite brojeve u kvadratnim korijenu.

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

Pomnožite 3750 i 167 da biste dobili 626250.

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

Izračunajte koliko je -27 na 10 da biste dobili \frac{1}{1000000000000000000000000000}.

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

Pomnožite 167 i \frac{1}{1000000000000000000000000000} da biste dobili \frac{167}{1000000000000000000000000000}.

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

Izračunajte koliko je 8 na 10 da biste dobili 100000000.

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

Pomnožite 3 i 100000000 da biste dobili 300000000.

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

Izračunajte koliko je 2 na 300000000 da biste dobili 90000000000000000.

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

Pomnožite \frac{167}{1000000000000000000000000000} i 90000000000000000 da biste dobili \frac{1503}{100000000000}.

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

Pomnožite \frac{1503}{100000000000} i \frac{\sqrt{13046875000000008517}}{626250} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Skratite 501 u brojniku i nazivniku.

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

Pomnožite 1250 i 100000000000 da biste dobili 125000000000000.

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