Riješi sqrt{292114*10^36/296*10^-19}

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

Izračunaj

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

Koraci rješenja

Skratite 2 u brojniku i nazivniku.

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

Da biste podijelili potencije s istom bazom, oduzmite eksponent nazivnika od eksponenta brojnika.

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

Izračunajte koliko je 55 na 10 da biste dobili 10000000000000000000000000000000000000000000000000000000.

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

Pomnožite 146057 i 10000000000000000000000000000000000000000000000000000000 da biste dobili 1460570000000000000000000000000000000000000000000000000000000.

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

Skratite razlomak \frac{1460570000000000000000000000000000000000000000000000000000000}{148} na najmanje vrijednosti tako da izlučite i poništite 4.

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

Ponovno napišite kvadratni korijen dijeljenja \sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}} kao dijeljenje kvadrata korijena \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

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

Rastavite 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570 na faktore. Ponovno napišite kvadratni korijen proizvoda \sqrt{500000000000000000000000000^{2}\times 1460570} kao umnožak kvadrata korijena \sqrt{500000000000000000000000000^{2}}\sqrt{1460570}. Izračunajte kvadratni korijen od 500000000000000000000000000^{2}.

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

Racionalizirajte nazivnik \frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} množenje brojnik i nazivnik \sqrt{37}.

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

Kvadrat od \sqrt{37} je 37.

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

Da biste pomnožite \sqrt{1460570} i \sqrt{37}, pomnožite brojeve u kvadratnim korijenu.

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