Lutasin ang sqrt{2.92114*10^36/2.96*10^-19}

$$\sqrt{ \frac{ 2.92114 \times { 10 }^{ 36 } }{ 2.96 \times { 10 }^{ -19 } } }$$

I-evaluate

$$\frac{50000000000000000000000000\sqrt{5404109}}{37}\approx 3.141451291 \cdot 10^{27}$$

Mga Hakbang ng Solution

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

$$\sqrt{\frac{2.92114\times 10^{55}}{2.96}}$$

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

$$\sqrt{\frac{2.92114\times 10000000000000000000000000000000000000000000000000000000}{2.96}}$$

I-multiply ang 2.92114 at 10000000000000000000000000000000000000000000000000000000 para makuha ang 29211400000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{29211400000000000000000000000000000000000000000000000000}{2.96}}$$

I-expand ang \frac{29211400000000000000000000000000000000000000000000000000}{2.96} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 100.

$$\sqrt{\frac{2921140000000000000000000000000000000000000000000000000000}{296}}$$

Bawasan ang fraction \frac{2921140000000000000000000000000000000000000000000000000000}{296} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 8.

$$\sqrt{\frac{365142500000000000000000000000000000000000000000000000000}{37}}$$

I-rewrite ang square root ng division na \sqrt{\frac{365142500000000000000000000000000000000000000000000000000}{37}} bilang division ng mga square root na \frac{\sqrt{365142500000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

$$\frac{\sqrt{365142500000000000000000000000000000000000000000000000000}}{\sqrt{37}}$$

I-factor out ang 365142500000000000000000000000000000000000000000000000000=50000000000000000000000000^{2}\times 146057. I-rewrite ang square root ng product na \sqrt{50000000000000000000000000^{2}\times 146057} bilang product ng mga square root na \sqrt{50000000000000000000000000^{2}}\sqrt{146057}. Kunin ang square root ng 50000000000000000000000000^{2}.

$$\frac{50000000000000000000000000\sqrt{146057}}{\sqrt{37}}$$

I-rationalize ang denominator ng \frac{50000000000000000000000000\sqrt{146057}}{\sqrt{37}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{37}.

$$\frac{50000000000000000000000000\sqrt{146057}\sqrt{37}}{\left(\sqrt{37}\right)^{2}}$$

Ang square ng \sqrt{37} ay 37.

$$\frac{50000000000000000000000000\sqrt{146057}\sqrt{37}}{37}$$

Para i-multiply ang \sqrt{146057} at \sqrt{37}, i-multiply ang mga numero sa ilalim ng square root.

$$\frac{50000000000000000000000000\sqrt{5404109}}{37}$$