Solve sqrt{2*1.6*10^-19*500/9.1*10^31}

$$\sqrt{ \frac{ 2 \times 1.6 \times { 10 }^{ -19 } \times 500 }{ 9.1 \times { 10 }^{ 31 } } }$$

Evaluate

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

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\sqrt{\frac{1.6\times 2\times 500}{9.1\times 10^{50}}}$$

Multiply 1.6 and 2 to get 3.2.

$$\sqrt{\frac{3.2\times 500}{9.1\times 10^{50}}}$$

Multiply 3.2 and 500 to get 1600.

$$\sqrt{\frac{1600}{9.1\times 10^{50}}}$$

Calculate 10 to the power of 50 and get 100000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{1600}{9.1\times 100000000000000000000000000000000000000000000000000}}$$

Multiply 9.1 and 100000000000000000000000000000000000000000000000000 to get 910000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{1600}{910000000000000000000000000000000000000000000000000}}$$

Reduce the fraction \frac{1600}{910000000000000000000000000000000000000000000000000} to lowest terms by extracting and canceling out 1600.

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

Rewrite the square root of the division \sqrt{\frac{1}{568750000000000000000000000000000000000000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{568750000000000000000000000000000000000000000000}}.

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

Calculate the square root of 1 and get 1.

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

Factor 568750000000000000000000000000000000000000000000=25000000000000000000000^{2}\times 910. Rewrite the square root of the product \sqrt{25000000000000000000000^{2}\times 910} as the product of square roots \sqrt{25000000000000000000000^{2}}\sqrt{910}. Take the square root of 25000000000000000000000^{2}.

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

Rationalize the denominator of \frac{1}{25000000000000000000000\sqrt{910}} by multiplying numerator and denominator by \sqrt{910}.

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

The square of \sqrt{910} is 910.

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

Multiply 25000000000000000000000 and 910 to get 22750000000000000000000000.

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