Riješi sqrt{292114*10^36/296*10^-19}

$$\sqrt{ \frac{ 292114 \times { 10 }^{ 36 } }{ 296 \times { 10 }^{ -19 } } }$$

Procijeni

$$\frac{500000000000000000000000000\sqrt{54041090}}{37}\approx 9,934141239 \cdot 10^{28}$$

Koraci za rješenje

Otkaži 2 u brojiocu i imeniocu.

$$\sqrt{\frac{146057\times 10^{36}}{148\times 10^{-19}}}$$

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

$$\sqrt{\frac{146057\times 10^{55}}{148}}$$

Izračunajte 10 stepen od 55 i dobijte 10000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{146057\times 10000000000000000000000000000000000000000000000000000000}{148}}$$

Pomnožite 146057 i 10000000000000000000000000000000000000000000000000000000 da biste dobili 1460570000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{1460570000000000000000000000000000000000000000000000000000000}{148}}$$

Svedite razlomak \frac{1460570000000000000000000000000000000000000000000000000000000}{148} na najprostije elemente rastavlјanjem i kraćenjem 4.

$$\sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}}$$

Ponovo napišite kvadratni korijen dijeljenja \sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}} kao dijeljenje kvadratnih korijena \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

$$\frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}$$

Faktorirajte 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570. Ponovo napišite kvadratni korijen proizvoda \sqrt{500000000000000000000000000^{2}\times 1460570} kao proizvod kvadratnih korijena \sqrt{500000000000000000000000000^{2}}\sqrt{1460570}. Izračunajte kvadratni korijen od 500000000000000000000000000^{2}.

$$\frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}}$$

Racionalizirajte imenilac broja \frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} tako što ćete pomnožiti brojilac i imenilac sa \sqrt{37}.

$$\frac{500000000000000000000000000\sqrt{1460570}\sqrt{37}}{\left(\sqrt{37}\right)^{2}}$$

Kvadrat broja \sqrt{37} je 37.

$$\frac{500000000000000000000000000\sqrt{1460570}\sqrt{37}}{37}$$

Da biste pomnožili \sqrt{1460570} i \sqrt{37}, pomnožite brojeve u okviru kvadratnog korijena.

$$\frac{500000000000000000000000000\sqrt{54041090}}{37}$$