Solve sqrt{3.2*10^-19*50000/9.1*10^-31}

$$\sqrt { \frac { 3.2 \times 10 ^ { - 19 } \times 50000 } { 9.1 \times 10 ^ { - 31 } } }$$

Evaluate

$$\frac{400000000\sqrt{910}}{91}\approx 132598708.826359168$$

Solution Steps

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

$$\sqrt{\frac{3.2\times 50000\times 10^{12}}{9.1}}$$

Multiply 3.2 and 50000 to get 160000.

$$\sqrt{\frac{160000\times 10^{12}}{9.1}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\sqrt{\frac{160000\times 1000000000000}{9.1}}$$

Multiply 160000 and 1000000000000 to get 160000000000000000.

$$\sqrt{\frac{160000000000000000}{9.1}}$$

Expand \frac{160000000000000000}{9.1} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{1600000000000000000}{91}}$$

Rewrite the square root of the division \sqrt{\frac{1600000000000000000}{91}} as the division of square roots \frac{\sqrt{1600000000000000000}}{\sqrt{91}}.

$$\frac{\sqrt{1600000000000000000}}{\sqrt{91}}$$

Factor 1600000000000000000=400000000^{2}\times 10. Rewrite the square root of the product \sqrt{400000000^{2}\times 10} as the product of square roots \sqrt{400000000^{2}}\sqrt{10}. Take the square root of 400000000^{2}.

$$\frac{400000000\sqrt{10}}{\sqrt{91}}$$

Rationalize the denominator of \frac{400000000\sqrt{10}}{\sqrt{91}} by multiplying numerator and denominator by \sqrt{91}.

$$\frac{400000000\sqrt{10}\sqrt{91}}{\left(\sqrt{91}\right)^{2}}$$

The square of \sqrt{91} is 91.

$$\frac{400000000\sqrt{10}\sqrt{91}}{91}$$

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

$$\frac{400000000\sqrt{910}}{91}$$