Rešite sqrt{2*16*10^-19*500/91*10^31}

$$\sqrt{ \frac{ 2 \times 16 \times { 10 }^{ -19 } \times 500 }{ 91 \times { 10 }^{ 31 } } }$$

Ovrednoti

$$\frac{\sqrt{910}}{22750000000000000000000000}\approx 1,325987088 \cdot 10^{-24}$$

Koraki rešitve

Če želite deliti potence enake osnove, odštejte eksponent števca od eksponenta imenovalca.

$$\sqrt{\frac{2\times 16\times 500}{91\times 10^{50}}}$$

Pomnožite 2 in 16, da dobite 32.

$$\sqrt{\frac{32\times 500}{91\times 10^{50}}}$$

Pomnožite 32 in 500, da dobite 16000.

$$\sqrt{\frac{16000}{91\times 10^{50}}}$$

Izračunajte potenco 10 števila 50, da dobite 100000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{16000}{91\times 100000000000000000000000000000000000000000000000000}}$$

Pomnožite 91 in 100000000000000000000000000000000000000000000000000, da dobite 9100000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{16000}{9100000000000000000000000000000000000000000000000000}}$$

Zmanjšajte ulomek \frac{16000}{9100000000000000000000000000000000000000000000000000} na najmanjši imenovalec tako, da izpeljete in okrajšate 16000.

$$\sqrt{\frac{1}{568750000000000000000000000000000000000000000000}}$$

Znova napišite kvadratni koren deljenja \sqrt{\frac{1}{568750000000000000000000000000000000000000000000}} kot deljenje kvadratnih korenov \frac{\sqrt{1}}{\sqrt{568750000000000000000000000000000000000000000000}}.

$$\frac{\sqrt{1}}{\sqrt{568750000000000000000000000000000000000000000000}}$$

Izračunajte kvadratni koren števila 1 in dobite 1.

$$\frac{1}{\sqrt{568750000000000000000000000000000000000000000000}}$$

Faktorizirajte 568750000000000000000000000000000000000000000000=25000000000000000000000^{2}\times 910. Znova napišite kvadratni koren izdelka \sqrt{25000000000000000000000^{2}\times 910} kot produkt kvadratnih korenov \sqrt{25000000000000000000000^{2}}\sqrt{910}. Uporabite kvadratni koren števila 25000000000000000000000^{2}.

$$\frac{1}{25000000000000000000000\sqrt{910}}$$

Racionalizirajte imenovalec \frac{1}{25000000000000000000000\sqrt{910}} tako, da pomnožite števec in imenovalec s \sqrt{910}.

$$\frac{\sqrt{910}}{25000000000000000000000\left(\sqrt{910}\right)^{2}}$$

Kvadrat vrednosti \sqrt{910} je 910.

$$\frac{\sqrt{910}}{25000000000000000000000\times 910}$$

Pomnožite 25000000000000000000000 in 910, da dobite 22750000000000000000000000.

$$\frac{\sqrt{910}}{22750000000000000000000000}$$