Rešite sqrt{4/3*55*10^-9*667*10^-11*314}

$$\sqrt { \frac { 4 } { 3 } \times 55 \times 10 ^ { - 9 } \times 667 \times 10 ^ { - 11 } \times 314 }$$

Ovrednoti

$$\frac{\sqrt{34557270}}{15000000000}\approx 0,000000392$$

Koraki rešitve

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte -9 in -11, da dobite -20.

$$\sqrt{\frac{4}{3}\times 55\times 10^{-20}\times 667\times 314}$$

Pomnožite \frac{4}{3} in 55, da dobite \frac{220}{3}.

$$\sqrt{\frac{220}{3}\times 10^{-20}\times 667\times 314}$$

Izračunajte potenco 10 števila -20, da dobite \frac{1}{100000000000000000000}.

$$\sqrt{\frac{220}{3}\times \frac{1}{100000000000000000000}\times 667\times 314}$$

Pomnožite \frac{220}{3} in \frac{1}{100000000000000000000}, da dobite \frac{11}{15000000000000000000}.

$$\sqrt{\frac{11}{15000000000000000000}\times 667\times 314}$$

Pomnožite \frac{11}{15000000000000000000} in 667, da dobite \frac{7337}{15000000000000000000}.

$$\sqrt{\frac{7337}{15000000000000000000}\times 314}$$

Pomnožite \frac{7337}{15000000000000000000} in 314, da dobite \frac{1151909}{7500000000000000000}.

$$\sqrt{\frac{1151909}{7500000000000000000}}$$

Znova napišite kvadratni koren deljenja \sqrt{\frac{1151909}{7500000000000000000}} kot deljenje kvadratnih korenov \frac{\sqrt{1151909}}{\sqrt{7500000000000000000}}.

$$\frac{\sqrt{1151909}}{\sqrt{7500000000000000000}}$$

Faktorizirajte 7500000000000000000=500000000^{2}\times 30. Znova napišite kvadratni koren izdelka \sqrt{500000000^{2}\times 30} kot produkt kvadratnih korenov \sqrt{500000000^{2}}\sqrt{30}. Uporabite kvadratni koren števila 500000000^{2}.

$$\frac{\sqrt{1151909}}{500000000\sqrt{30}}$$

Racionalizirajte imenovalec \frac{\sqrt{1151909}}{500000000\sqrt{30}} tako, da pomnožite števec in imenovalec s \sqrt{30}.

$$\frac{\sqrt{1151909}\sqrt{30}}{500000000\left(\sqrt{30}\right)^{2}}$$

Kvadrat vrednosti \sqrt{30} je 30.

$$\frac{\sqrt{1151909}\sqrt{30}}{500000000\times 30}$$

Če želite \sqrt{1151909} pomnožite in \sqrt{30}, pomnožite številke v kvadratni korenu.

$$\frac{\sqrt{34557270}}{500000000\times 30}$$

Pomnožite 500000000 in 30, da dobite 15000000000.

$$\frac{\sqrt{34557270}}{15000000000}$$