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

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

Evaluate

$$\frac{40000000\sqrt{910}}{91}\approx 13259870.882635918$$

Solution Steps

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

$$\sqrt{\frac{1.6\times 2\times 500\times 10^{12}}{9.1}}$$

Multiply 1.6 and 2 to get 3.2.

$$\sqrt{\frac{3.2\times 500\times 10^{12}}{9.1}}$$

Multiply 3.2 and 500 to get 1600.

$$\sqrt{\frac{1600\times 10^{12}}{9.1}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\sqrt{\frac{1600\times 1000000000000}{9.1}}$$

Multiply 1600 and 1000000000000 to get 1600000000000000.

$$\sqrt{\frac{1600000000000000}{9.1}}$$

Expand \frac{1600000000000000}{9.1} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{16000000000000000}{91}}$$

Rewrite the square root of the division \sqrt{\frac{16000000000000000}{91}} as the division of square roots \frac{\sqrt{16000000000000000}}{\sqrt{91}}.

$$\frac{\sqrt{16000000000000000}}{\sqrt{91}}$$

Factor 16000000000000000=40000000^{2}\times 10. Rewrite the square root of the product \sqrt{40000000^{2}\times 10} as the product of square roots \sqrt{40000000^{2}}\sqrt{10}. Take the square root of 40000000^{2}.

$$\frac{40000000\sqrt{10}}{\sqrt{91}}$$

Rationalize the denominator of \frac{40000000\sqrt{10}}{\sqrt{91}} by multiplying numerator and denominator by \sqrt{91}.

$$\frac{40000000\sqrt{10}\sqrt{91}}{\left(\sqrt{91}\right)^{2}}$$

The square of \sqrt{91} is 91.

$$\frac{40000000\sqrt{10}\sqrt{91}}{91}$$

To multiply \sqrt{10} and \sqrt{91}, multiply the numbers under the square root.

$$\frac{40000000\sqrt{910}}{91}$$