Solve sqrt{2*0.12*1.602*10^-19/9.109*10^-31}

$$\sqrt{ \frac{ 2 \times 0.12 \times 1.602 \times { 10 }^{ -19 } }{ 9.109 \times { 10 }^{ -31 } } }$$

Evaluate

$$\frac{1200000\sqrt{2432103}}{9109}\approx 205447.814490898$$

Solution Steps

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

$$\sqrt{\frac{0.12\times 1.602\times 2\times 10^{12}}{9.109}}$$

Multiply 0.12 and 1.602 to get 0.19224.

$$\sqrt{\frac{0.19224\times 2\times 10^{12}}{9.109}}$$

Multiply 0.19224 and 2 to get 0.38448.

$$\sqrt{\frac{0.38448\times 10^{12}}{9.109}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\sqrt{\frac{0.38448\times 1000000000000}{9.109}}$$

Multiply 0.38448 and 1000000000000 to get 384480000000.

$$\sqrt{\frac{384480000000}{9.109}}$$

Expand \frac{384480000000}{9.109} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{384480000000000}{9109}}$$

Rewrite the square root of the division \sqrt{\frac{384480000000000}{9109}} as the division of square roots \frac{\sqrt{384480000000000}}{\sqrt{9109}}.

$$\frac{\sqrt{384480000000000}}{\sqrt{9109}}$$

Factor 384480000000000=1200000^{2}\times 267. Rewrite the square root of the product \sqrt{1200000^{2}\times 267} as the product of square roots \sqrt{1200000^{2}}\sqrt{267}. Take the square root of 1200000^{2}.

$$\frac{1200000\sqrt{267}}{\sqrt{9109}}$$

Rationalize the denominator of \frac{1200000\sqrt{267}}{\sqrt{9109}} by multiplying numerator and denominator by \sqrt{9109}.

$$\frac{1200000\sqrt{267}\sqrt{9109}}{\left(\sqrt{9109}\right)^{2}}$$

The square of \sqrt{9109} is 9109.

$$\frac{1200000\sqrt{267}\sqrt{9109}}{9109}$$

To multiply \sqrt{267} and \sqrt{9109}, multiply the numbers under the square root.

$$\frac{1200000\sqrt{2432103}}{9109}$$