Leysa sqrt{292114*10^36/296*10^-19}

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

Meta

$$\frac{500000000000000000000000000\sqrt{54041090}}{37}\approx 9.934141239 \cdot 10^{28}$$

Lausnarskref

Styttu burt 2 í bæði teljara og samnefnara.

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

Dragðu veldisvísi nefnarans frá veldisvísi teljarans til að deila veldum með sama stofn.

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

Reiknaðu 10 í 55. veldi og fáðu 10000000000000000000000000000000000000000000000000000000.

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

Margfaldaðu 146057 og 10000000000000000000000000000000000000000000000000000000 til að fá út 1460570000000000000000000000000000000000000000000000000000000.

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

Minnka brotið \frac{1460570000000000000000000000000000000000000000000000000000000}{148} eins mikið og hægt er með því að draga og stytta út 4.

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

Endurskrifaðu kvaðratrót deilingar \sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}} sem deilingu kvaðratróta \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

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

Stuðull 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570. Endurskrifaðu kvaðratrót margfeldis \sqrt{500000000000000000000000000^{2}\times 1460570} sem margfeldi kvaðratróta \sqrt{500000000000000000000000000^{2}}\sqrt{1460570}. Finndu kvaðratrót 500000000000000000000000000^{2}.

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

Gerðu nefnara \frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} að ræðri tölu með því að margfalda teljarann og nefnarann með \sqrt{37}.

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

\sqrt{37} í öðru veldi er 37.

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

Til að margfalda \sqrt{1460570} og \sqrt{37} skaltu margfalda tölurnar undir kvaðratrótinni.

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