Rešite sqrt{292114*10^36/296*10^-19}

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

Ovrednoti

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

Koraki rešitve

Okrajšaj 2 v števcu in imenovalcu.

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

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

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

Izračunajte potenco 10 števila 55, da dobite 10000000000000000000000000000000000000000000000000000000.

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

Pomnožite 146057 in 10000000000000000000000000000000000000000000000000000000, da dobite 1460570000000000000000000000000000000000000000000000000000000.

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

Zmanjšajte ulomek \frac{1460570000000000000000000000000000000000000000000000000000000}{148} na najmanjši imenovalec tako, da izpeljete in okrajšate 4.

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

Znova napišite kvadratni koren deljenja \sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}} kot deljenje kvadratnih korenov \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

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

Faktorizirajte 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570. Znova napišite kvadratni koren izdelka \sqrt{500000000000000000000000000^{2}\times 1460570} kot produkt kvadratnih korenov \sqrt{500000000000000000000000000^{2}}\sqrt{1460570}. Uporabite kvadratni koren števila 500000000000000000000000000^{2}.

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

Racionalizirajte imenovalec \frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} tako, da pomnožite števec in imenovalec s \sqrt{37}.

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

Kvadrat vrednosti \sqrt{37} je 37.

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

Če želite \sqrt{1460570} pomnožite in \sqrt{37}, pomnožite številke v kvadratni korenu.

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