Solve sqrt{9*10^9*(1.6*10^-19)^2/0.53*10^-10}

$$\sqrt { \frac { 9 \times 10 ^ { 9 } \times ( 1.6 \times 10 ^ { - 19 } ) ^ { 2 } } { 0.53 \times 10 ^ { - 10 } } }$$

Evaluate

$$\frac{3\sqrt{530}}{33125000000}\approx 2.084986765 \cdot 10^{-9}$$

Solution Steps

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

$$\sqrt{\frac{9\times 10^{19}\times \left(1.6\times 10^{-19}\right)^{2}}{0.53}}$$

Calculate 10 to the power of 19 and get 10000000000000000000.

$$\sqrt{\frac{9\times 10000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{0.53}}$$

Multiply 9 and 10000000000000000000 to get 90000000000000000000.

$$\sqrt{\frac{90000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{0.53}}$$

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$\sqrt{\frac{90000000000000000000\times \left(1.6\times \frac{1}{10000000000000000000}\right)^{2}}{0.53}}$$

Multiply 1.6 and \frac{1}{10000000000000000000} to get \frac{1}{6250000000000000000}.

$$\sqrt{\frac{90000000000000000000\times \left(\frac{1}{6250000000000000000}\right)^{2}}{0.53}}$$

Calculate \frac{1}{6250000000000000000} to the power of 2 and get \frac{1}{39062500000000000000000000000000000000}.

$$\sqrt{\frac{90000000000000000000\times \frac{1}{39062500000000000000000000000000000000}}{0.53}}$$

Multiply 90000000000000000000 and \frac{1}{39062500000000000000000000000000000000} to get \frac{9}{3906250000000000000}.

$$\sqrt{\frac{\frac{9}{3906250000000000000}}{0.53}}$$

Express \frac{\frac{9}{3906250000000000000}}{0.53} as a single fraction.

$$\sqrt{\frac{9}{3906250000000000000\times 0.53}}$$

Multiply 3906250000000000000 and 0.53 to get 2070312500000000000.

$$\sqrt{\frac{9}{2070312500000000000}}$$

Rewrite the square root of the division \sqrt{\frac{9}{2070312500000000000}} as the division of square roots \frac{\sqrt{9}}{\sqrt{2070312500000000000}}.

$$\frac{\sqrt{9}}{\sqrt{2070312500000000000}}$$

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{2070312500000000000}}$$

Factor 2070312500000000000=62500000^{2}\times 530. Rewrite the square root of the product \sqrt{62500000^{2}\times 530} as the product of square roots \sqrt{62500000^{2}}\sqrt{530}. Take the square root of 62500000^{2}.

$$\frac{3}{62500000\sqrt{530}}$$

Rationalize the denominator of \frac{3}{62500000\sqrt{530}} by multiplying numerator and denominator by \sqrt{530}.

$$\frac{3\sqrt{530}}{62500000\left(\sqrt{530}\right)^{2}}$$

The square of \sqrt{530} is 530.

$$\frac{3\sqrt{530}}{62500000\times 530}$$

Multiply 62500000 and 530 to get 33125000000.

$$\frac{3\sqrt{530}}{33125000000}$$