Lutasin ang sqrt{2*16*10^-19*500/91*10^31}

$$\sqrt{ \frac{ 2 \times 16 \times { 10 }^{ -19 } \times 500 }{ 91 \times { 10 }^{ 31 } } }$$

I-evaluate

$$\frac{\sqrt{910}}{22750000000000000000000000}\approx 1.325987088 \cdot 10^{-24}$$

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.

$$\sqrt{\frac{2\times 16\times 500}{91\times 10^{50}}}$$

I-multiply ang 2 at 16 para makuha ang 32.

$$\sqrt{\frac{32\times 500}{91\times 10^{50}}}$$

I-multiply ang 32 at 500 para makuha ang 16000.

$$\sqrt{\frac{16000}{91\times 10^{50}}}$$

Kalkulahin ang 10 sa power ng 50 at kunin ang 100000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{16000}{91\times 100000000000000000000000000000000000000000000000000}}$$

I-multiply ang 91 at 100000000000000000000000000000000000000000000000000 para makuha ang 9100000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{16000}{9100000000000000000000000000000000000000000000000000}}$$

Bawasan ang fraction \frac{16000}{9100000000000000000000000000000000000000000000000000} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 16000.

$$\sqrt{\frac{1}{568750000000000000000000000000000000000000000000}}$$

I-rewrite ang square root ng division na \sqrt{\frac{1}{568750000000000000000000000000000000000000000000}} bilang division ng mga square root na \frac{\sqrt{1}}{\sqrt{568750000000000000000000000000000000000000000000}}.

$$\frac{\sqrt{1}}{\sqrt{568750000000000000000000000000000000000000000000}}$$

Kalkulahin ang square root ng 1 at makuha ang 1.

$$\frac{1}{\sqrt{568750000000000000000000000000000000000000000000}}$$

I-factor out ang 568750000000000000000000000000000000000000000000=25000000000000000000000^{2}\times 910. I-rewrite ang square root ng product na \sqrt{25000000000000000000000^{2}\times 910} bilang product ng mga square root na \sqrt{25000000000000000000000^{2}}\sqrt{910}. Kunin ang square root ng 25000000000000000000000^{2}.

$$\frac{1}{25000000000000000000000\sqrt{910}}$$

I-rationalize ang denominator ng \frac{1}{25000000000000000000000\sqrt{910}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{910}.

$$\frac{\sqrt{910}}{25000000000000000000000\left(\sqrt{910}\right)^{2}}$$

Ang square ng \sqrt{910} ay 910.

$$\frac{\sqrt{910}}{25000000000000000000000\times 910}$$

I-multiply ang 25000000000000000000000 at 910 para makuha ang 22750000000000000000000000.

$$\frac{\sqrt{910}}{22750000000000000000000000}$$