Solve 6*63*10^-34/1.67*10^-27*sqrt{frac{3*1.09*10^7{2*10^-3}*300}}

$$\frac { 6 \cdot 63 \times 10 ^ { - 34 } } { 1.67 \times 10 ^ { - 27 } \cdot \sqrt { \frac { 3 \times 1.09 \times 10 ^ { 7 } } { 2 \times 10 ^ { - 3 } } \times 300 } }$$

Evaluate

$$\frac{63\sqrt{218}}{91015000000000}\approx 1.022011595 \cdot 10^{-11}$$

Solution Steps

Multiply 6 and 63 to get 378.

$$\frac{378\times 10^{-34}}{1.67\times 10^{-27}\sqrt{\frac{3\times 1.09\times 10^{7}}{2\times 10^{-3}}\times 300}}$$

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

$$\frac{378\times \frac{1}{10000000000000000000000000000000000}}{1.67\times 10^{-27}\sqrt{\frac{3\times 1.09\times 10^{7}}{2\times 10^{-3}}\times 300}}$$

Multiply 378 and \frac{1}{10000000000000000000000000000000000} to get \frac{189}{5000000000000000000000000000000000}.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{1.67\times 10^{-27}\sqrt{\frac{3\times 1.09\times 10^{7}}{2\times 10^{-3}}\times 300}}$$

Calculate 10 to the power of -27 and get \frac{1}{1000000000000000000000000000}.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{1.67\times \frac{1}{1000000000000000000000000000}\sqrt{\frac{3\times 1.09\times 10^{7}}{2\times 10^{-3}}\times 300}}$$

Multiply 1.67 and \frac{1}{1000000000000000000000000000} to get \frac{167}{100000000000000000000000000000}.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{\frac{167}{100000000000000000000000000000}\sqrt{\frac{3\times 1.09\times 10^{7}}{2\times 10^{-3}}\times 300}}$$

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

$$\frac{\frac{189}{5000000000000000000000000000000000}}{\frac{167}{100000000000000000000000000000}\sqrt{\frac{1.09\times 3\times 10^{10}}{2}\times 300}}$$

Multiply 1.09 and 3 to get 3.27.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{\frac{167}{100000000000000000000000000000}\sqrt{\frac{3.27\times 10^{10}}{2}\times 300}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{\frac{167}{100000000000000000000000000000}\sqrt{\frac{3.27\times 10000000000}{2}\times 300}}$$

Multiply 3.27 and 10000000000 to get 32700000000.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{\frac{167}{100000000000000000000000000000}\sqrt{\frac{32700000000}{2}\times 300}}$$

Divide 32700000000 by 2 to get 16350000000.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{\frac{167}{100000000000000000000000000000}\sqrt{16350000000\times 300}}$$

Multiply 16350000000 and 300 to get 4905000000000.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{\frac{167}{100000000000000000000000000000}\sqrt{4905000000000}}$$

Factor 4905000000000=150000^{2}\times 218. Rewrite the square root of the product \sqrt{150000^{2}\times 218} as the product of square roots \sqrt{150000^{2}}\sqrt{218}. Take the square root of 150000^{2}.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{\frac{167}{100000000000000000000000000000}\times 150000\sqrt{218}}$$

Multiply \frac{167}{100000000000000000000000000000} and 150000 to get \frac{501}{2000000000000000000000000}.

$$\frac{\frac{189}{5000000000000000000000000000000000}}{\frac{501}{2000000000000000000000000}\sqrt{218}}$$

Express \frac{\frac{189}{5000000000000000000000000000000000}}{\frac{501}{2000000000000000000000000}\sqrt{218}} as a single fraction.

$$\frac{189}{5000000000000000000000000000000000\times \frac{501}{2000000000000000000000000}\sqrt{218}}$$

Rationalize the denominator of \frac{189}{5000000000000000000000000000000000\times \frac{501}{2000000000000000000000000}\sqrt{218}} by multiplying numerator and denominator by \sqrt{218}.

$$\frac{189\sqrt{218}}{5000000000000000000000000000000000\times \frac{501}{2000000000000000000000000}\left(\sqrt{218}\right)^{2}}$$

The square of \sqrt{218} is 218.

$$\frac{189\sqrt{218}}{5000000000000000000000000000000000\times \frac{501}{2000000000000000000000000}\times 218}$$

Multiply 5000000000000000000000000000000000 and \frac{501}{2000000000000000000000000} to get 1252500000000.

$$\frac{189\sqrt{218}}{1252500000000\times 218}$$

Multiply 1252500000000 and 218 to get 273045000000000.

$$\frac{189\sqrt{218}}{273045000000000}$$

Divide 189\sqrt{218} by 273045000000000 to get \frac{63}{91015000000000}\sqrt{218}.

$$\frac{63}{91015000000000}\sqrt{218}$$