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

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

I-evaluate

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

Mga Hakbang ng Solution

I-cancel out ang 2 sa parehong numerator at denominator.

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

Para magi-divide ng mga power na may parehong base, i-subtract ang exponent ng denominator mula sa exponent ng numerator.

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

Kalkulahin ang 10 sa power ng 55 at kunin ang 10000000000000000000000000000000000000000000000000000000.

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

I-multiply ang 146057 at 10000000000000000000000000000000000000000000000000000000 para makuha ang 1460570000000000000000000000000000000000000000000000000000000.

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

Bawasan ang fraction \frac{1460570000000000000000000000000000000000000000000000000000000}{148} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 4.

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

I-rewrite ang square root ng division na \sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}} bilang division ng mga square root na \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

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

I-factor out ang 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570. I-rewrite ang square root ng product na \sqrt{500000000000000000000000000^{2}\times 1460570} bilang product ng mga square root na \sqrt{500000000000000000000000000^{2}}\sqrt{1460570}. Kunin ang square root ng 500000000000000000000000000^{2}.

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

I-rationalize ang denominator ng \frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{37}.

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

Ang square ng \sqrt{37} ay 37.

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

Para i-multiply ang \sqrt{1460570} at \sqrt{37}, i-multiply ang mga numero sa ilalim ng square root.

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