Solve 6.626*10^-34/sqrt{(2(9.11*10^-31)(100)(1.6*10^-19))}

$$\frac{ 6.626 \times { 10 }^{ -34 } }{ \sqrt{ (2(9.11 \times { 10 }^{ -31 } )(100)(1.6 \times { 10 }^{ -19 } )) } }$$

Evaluate

$$\frac{3313\sqrt{4555}}{1822000000000000}\approx 1.22720539 \cdot 10^{-10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -31 and -19 to get -50.

$$\frac{6.626\times 10^{-34}}{\sqrt{2\times 9.11\times 10^{-50}\times 100\times 1.6}}$$

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$\frac{6.626\times \frac{1}{10000000000000000000000000000000000}}{\sqrt{2\times 9.11\times 10^{-50}\times 100\times 1.6}}$$

Multiply 6.626 and \frac{1}{10000000000000000000000000000000000} to get \frac{3313}{5000000000000000000000000000000000000}.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\sqrt{2\times 9.11\times 10^{-50}\times 100\times 1.6}}$$

Multiply 2 and 9.11 to get 18.22.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\sqrt{18.22\times 10^{-50}\times 100\times 1.6}}$$

Calculate 10 to the power of -50 and get \frac{1}{100000000000000000000000000000000000000000000000000}.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\sqrt{18.22\times \frac{1}{100000000000000000000000000000000000000000000000000}\times 100\times 1.6}}$$

Multiply 18.22 and \frac{1}{100000000000000000000000000000000000000000000000000} to get \frac{911}{5000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\sqrt{\frac{911}{5000000000000000000000000000000000000000000000000000}\times 100\times 1.6}}$$

Multiply \frac{911}{5000000000000000000000000000000000000000000000000000} and 100 to get \frac{911}{50000000000000000000000000000000000000000000000000}.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\sqrt{\frac{911}{50000000000000000000000000000000000000000000000000}\times 1.6}}$$

Multiply \frac{911}{50000000000000000000000000000000000000000000000000} and 1.6 to get \frac{911}{31250000000000000000000000000000000000000000000000}.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\sqrt{\frac{911}{31250000000000000000000000000000000000000000000000}}}$$

Rewrite the square root of the division \sqrt{\frac{911}{31250000000000000000000000000000000000000000000000}} as the division of square roots \frac{\sqrt{911}}{\sqrt{31250000000000000000000000000000000000000000000000}}.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\frac{\sqrt{911}}{\sqrt{31250000000000000000000000000000000000000000000000}}}$$

Factor 31250000000000000000000000000000000000000000000000=2500000000000000000000000^{2}\times 5. Rewrite the square root of the product \sqrt{2500000000000000000000000^{2}\times 5} as the product of square roots \sqrt{2500000000000000000000000^{2}}\sqrt{5}. Take the square root of 2500000000000000000000000^{2}.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\frac{\sqrt{911}}{2500000000000000000000000\sqrt{5}}}$$

Rationalize the denominator of \frac{\sqrt{911}}{2500000000000000000000000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\frac{\sqrt{911}\sqrt{5}}{2500000000000000000000000\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\frac{\sqrt{911}\sqrt{5}}{2500000000000000000000000\times 5}}$$

To multiply \sqrt{911} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\frac{\sqrt{4555}}{2500000000000000000000000\times 5}}$$

Multiply 2500000000000000000000000 and 5 to get 12500000000000000000000000.

$$\frac{\frac{3313}{5000000000000000000000000000000000000}}{\frac{\sqrt{4555}}{12500000000000000000000000}}$$

Divide \frac{3313}{5000000000000000000000000000000000000} by \frac{\sqrt{4555}}{12500000000000000000000000} by multiplying \frac{3313}{5000000000000000000000000000000000000} by the reciprocal of \frac{\sqrt{4555}}{12500000000000000000000000}.

$$\frac{3313\times 12500000000000000000000000}{5000000000000000000000000000000000000\sqrt{4555}}$$

Cancel out 12500000000000000000000000 in both numerator and denominator.

$$\frac{3313}{400000000000\sqrt{4555}}$$

Rationalize the denominator of \frac{3313}{400000000000\sqrt{4555}} by multiplying numerator and denominator by \sqrt{4555}.

$$\frac{3313\sqrt{4555}}{400000000000\left(\sqrt{4555}\right)^{2}}$$

The square of \sqrt{4555} is 4555.

$$\frac{3313\sqrt{4555}}{400000000000\times 4555}$$

Multiply 400000000000 and 4555 to get 1822000000000000.

$$\frac{3313\sqrt{4555}}{1822000000000000}$$