Solve 1/0.01sqrt{2*9.1*10^-31/1.6*10^-19}

$$\frac{ 1 }{ 0.01 } \sqrt{ \frac{ 2 \times 9.1 \times { 10 }^{ -31 } }{ 1.6 \times { 10 }^{ -19 } } }$$

Evaluate

$$\frac{\sqrt{182}}{40000}\approx 0.000337268$$

Solution Steps

Expand \frac{1}{0.01} by multiplying both numerator and the denominator by 100. Anything divided by one gives itself.

$$100\sqrt{\frac{2\times 9.1\times 10^{-31}}{1.6\times 10^{-19}}}$$

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

$$100\sqrt{\frac{2\times 9.1}{1.6\times 10^{12}}}$$

Multiply 2 and 9.1 to get 18.2.

$$100\sqrt{\frac{18.2}{1.6\times 10^{12}}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$100\sqrt{\frac{18.2}{1.6\times 1000000000000}}$$

Multiply 1.6 and 1000000000000 to get 1600000000000.

$$100\sqrt{\frac{18.2}{1600000000000}}$$

Expand \frac{18.2}{1600000000000} by multiplying both numerator and the denominator by 10.

$$100\sqrt{\frac{182}{16000000000000}}$$

Reduce the fraction \frac{182}{16000000000000} to lowest terms by extracting and canceling out 2.

$$100\sqrt{\frac{91}{8000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{91}{8000000000000}} as the division of square roots \frac{\sqrt{91}}{\sqrt{8000000000000}}.

$$100\times \frac{\sqrt{91}}{\sqrt{8000000000000}}$$

Factor 8000000000000=2000000^{2}\times 2. Rewrite the square root of the product \sqrt{2000000^{2}\times 2} as the product of square roots \sqrt{2000000^{2}}\sqrt{2}. Take the square root of 2000000^{2}.

$$100\times \frac{\sqrt{91}}{2000000\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{91}}{2000000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$100\times \frac{\sqrt{91}\sqrt{2}}{2000000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$100\times \frac{\sqrt{91}\sqrt{2}}{2000000\times 2}$$

To multiply \sqrt{91} and \sqrt{2}, multiply the numbers under the square root.

$$100\times \frac{\sqrt{182}}{2000000\times 2}$$

Multiply 2000000 and 2 to get 4000000.

$$100\times \frac{\sqrt{182}}{4000000}$$

Cancel out 4000000, the greatest common factor in 100 and 4000000.

$$\frac{\sqrt{182}}{40000}$$