Riješi frac{sqrt{2(216*10^-19}}{911*10^-31}

$$\frac { \sqrt { 2 ( 216 \times 10 ^ { - 19 } } } { 911 \times 10 ^ { - 31 } }$$

Procijeni

$$\frac{12000000000000000000000\sqrt{30}}{911}\approx 7,214786707 \cdot 10^{19}$$

Koraci za rješenje

Pomnožite 2 i 216 da biste dobili 432.

$$\frac{\sqrt{432\times 10^{-19}}}{911\times 10^{-31}}$$

Izračunajte 10 stepen od -19 i dobijte \frac{1}{10000000000000000000}.

$$\frac{\sqrt{432\times \frac{1}{10000000000000000000}}}{911\times 10^{-31}}$$

Pomnožite 432 i \frac{1}{10000000000000000000} da biste dobili \frac{27}{625000000000000000}.

$$\frac{\sqrt{\frac{27}{625000000000000000}}}{911\times 10^{-31}}$$

Ponovo napišite kvadratni korijen dijeljenja \sqrt{\frac{27}{625000000000000000}} kao dijeljenje kvadratnih korijena \frac{\sqrt{27}}{\sqrt{625000000000000000}}.

$$\frac{\frac{\sqrt{27}}{\sqrt{625000000000000000}}}{911\times 10^{-31}}$$

Faktorirajte 27=3^{2}\times 3. Ponovo napišite kvadratni korijen proizvoda \sqrt{3^{2}\times 3} kao proizvod kvadratnih korijena \sqrt{3^{2}}\sqrt{3}. Izračunajte kvadratni korijen od 3^{2}.

$$\frac{\frac{3\sqrt{3}}{\sqrt{625000000000000000}}}{911\times 10^{-31}}$$

Faktorirajte 625000000000000000=250000000^{2}\times 10. Ponovo napišite kvadratni korijen proizvoda \sqrt{250000000^{2}\times 10} kao proizvod kvadratnih korijena \sqrt{250000000^{2}}\sqrt{10}. Izračunajte kvadratni korijen od 250000000^{2}.

$$\frac{\frac{3\sqrt{3}}{250000000\sqrt{10}}}{911\times 10^{-31}}$$

Racionalizirajte imenilac broja \frac{3\sqrt{3}}{250000000\sqrt{10}} tako što ćete pomnožiti brojilac i imenilac sa \sqrt{10}.

$$\frac{\frac{3\sqrt{3}\sqrt{10}}{250000000\left(\sqrt{10}\right)^{2}}}{911\times 10^{-31}}$$

Kvadrat broja \sqrt{10} je 10.

$$\frac{\frac{3\sqrt{3}\sqrt{10}}{250000000\times 10}}{911\times 10^{-31}}$$

Da biste pomnožili \sqrt{3} i \sqrt{10}, pomnožite brojeve u okviru kvadratnog korijena.

$$\frac{\frac{3\sqrt{30}}{250000000\times 10}}{911\times 10^{-31}}$$

Pomnožite 250000000 i 10 da biste dobili 2500000000.

$$\frac{\frac{3\sqrt{30}}{2500000000}}{911\times 10^{-31}}$$

Izračunajte 10 stepen od -31 i dobijte \frac{1}{10000000000000000000000000000000}.

$$\frac{\frac{3\sqrt{30}}{2500000000}}{911\times \frac{1}{10000000000000000000000000000000}}$$

Pomnožite 911 i \frac{1}{10000000000000000000000000000000} da biste dobili \frac{911}{10000000000000000000000000000000}.

$$\frac{\frac{3\sqrt{30}}{2500000000}}{\frac{911}{10000000000000000000000000000000}}$$

Podijelite \frac{3\sqrt{30}}{2500000000} sa \frac{911}{10000000000000000000000000000000} tako što ćete pomnožiti \frac{3\sqrt{30}}{2500000000} recipročnom vrijednošću od \frac{911}{10000000000000000000000000000000}.

$$\frac{3\sqrt{30}\times 10000000000000000000000000000000}{2500000000\times 911}$$

Otkaži 2500000000 u brojiocu i imeniocu.

$$\frac{3\times 4000000000000000000000\sqrt{30}}{911}$$

Pomnožite 3 i 4000000000000000000000 da biste dobili 12000000000000000000000.

$$\frac{12000000000000000000000\sqrt{30}}{911}$$