Riješi sqrt{2*16*10^-19*500/91*10^31}

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

Procijeni

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

Koraci za rješenje

Da biste podijelili stepene iste osnove, oduzmite eksponent brojioca od eksponenta imenioca.

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

Pomnožite 2 i 16 da biste dobili 32.

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

Pomnožite 32 i 500 da biste dobili 16000.

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

Izračunajte 10 stepen od 50 i dobijte 100000000000000000000000000000000000000000000000000.

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

Pomnožite 91 i 100000000000000000000000000000000000000000000000000 da biste dobili 9100000000000000000000000000000000000000000000000000.

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

Svedite razlomak \frac{16000}{9100000000000000000000000000000000000000000000000000} na najprostije elemente rastavlјanjem i kraćenjem 16000.

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

Ponovo napišite kvadratni korijen dijeljenja \sqrt{\frac{1}{568750000000000000000000000000000000000000000000}} kao dijeljenje kvadratnih korijena \frac{\sqrt{1}}{\sqrt{568750000000000000000000000000000000000000000000}}.

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

Izračunajte kvadratni koren od 1 i dobijte 1.

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

Faktorirajte 568750000000000000000000000000000000000000000000=25000000000000000000000^{2}\times 910. Ponovo napišite kvadratni korijen proizvoda \sqrt{25000000000000000000000^{2}\times 910} kao proizvod kvadratnih korijena \sqrt{25000000000000000000000^{2}}\sqrt{910}. Izračunajte kvadratni korijen od 25000000000000000000000^{2}.

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

Racionalizirajte imenilac broja \frac{1}{25000000000000000000000\sqrt{910}} tako što ćete pomnožiti brojilac i imenilac sa \sqrt{910}.

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

Kvadrat broja \sqrt{910} je 910.

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

Pomnožite 25000000000000000000000 i 910 da biste dobili 22750000000000000000000000.

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