Solve sqrt{2*8.85*10^-140.7*11.9/1.610^-19}sqrt{1/10^17}

$$\sqrt{ \frac{ 2 \cdot 8.85 \times { 10 }^{ -14 } 0.7 \cdot 11.9 }{ 1.6 { 10 }^{ -19 } } } \sqrt{ \frac{ 1 }{ { 10 }^{ 17 } } }$$

Evaluate

$$\frac{7\sqrt{3009}}{40000000}\approx 0.0000096$$

Solution Steps

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

$$\sqrt{\frac{0.7\times 2\times 8.85\times 11.9\times 10^{5}}{1.6}}\sqrt{\frac{1}{10^{17}}}$$

Multiply 0.7 and 2 to get 1.4.

$$\sqrt{\frac{1.4\times 8.85\times 11.9\times 10^{5}}{1.6}}\sqrt{\frac{1}{10^{17}}}$$

Multiply 1.4 and 8.85 to get 12.39.

$$\sqrt{\frac{12.39\times 11.9\times 10^{5}}{1.6}}\sqrt{\frac{1}{10^{17}}}$$

Multiply 12.39 and 11.9 to get 147.441.

$$\sqrt{\frac{147.441\times 10^{5}}{1.6}}\sqrt{\frac{1}{10^{17}}}$$

Calculate 10 to the power of 5 and get 100000.

$$\sqrt{\frac{147.441\times 100000}{1.6}}\sqrt{\frac{1}{10^{17}}}$$

Multiply 147.441 and 100000 to get 14744100.

$$\sqrt{\frac{14744100}{1.6}}\sqrt{\frac{1}{10^{17}}}$$

Expand \frac{14744100}{1.6} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{147441000}{16}}\sqrt{\frac{1}{10^{17}}}$$

Reduce the fraction \frac{147441000}{16} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{18430125}{2}}\sqrt{\frac{1}{10^{17}}}$$

Rewrite the square root of the division \sqrt{\frac{18430125}{2}} as the division of square roots \frac{\sqrt{18430125}}{\sqrt{2}}.

$$\frac{\sqrt{18430125}}{\sqrt{2}}\sqrt{\frac{1}{10^{17}}}$$

Factor 18430125=35^{2}\times 15045. Rewrite the square root of the product \sqrt{35^{2}\times 15045} as the product of square roots \sqrt{35^{2}}\sqrt{15045}. Take the square root of 35^{2}.

$$\frac{35\sqrt{15045}}{\sqrt{2}}\sqrt{\frac{1}{10^{17}}}$$

Rationalize the denominator of \frac{35\sqrt{15045}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{35\sqrt{15045}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sqrt{\frac{1}{10^{17}}}$$

The square of \sqrt{2} is 2.

$$\frac{35\sqrt{15045}\sqrt{2}}{2}\sqrt{\frac{1}{10^{17}}}$$

To multiply \sqrt{15045} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{35\sqrt{30090}}{2}\sqrt{\frac{1}{10^{17}}}$$

Calculate 10 to the power of 17 and get 100000000000000000.

$$\frac{35\sqrt{30090}}{2}\sqrt{\frac{1}{100000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{100000000000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{100000000000000000}}.

$$\frac{35\sqrt{30090}}{2}\times \frac{\sqrt{1}}{\sqrt{100000000000000000}}$$

Calculate the square root of 1 and get 1.

$$\frac{35\sqrt{30090}}{2}\times \frac{1}{\sqrt{100000000000000000}}$$

Factor 100000000000000000=100000000^{2}\times 10. Rewrite the square root of the product \sqrt{100000000^{2}\times 10} as the product of square roots \sqrt{100000000^{2}}\sqrt{10}. Take the square root of 100000000^{2}.

$$\frac{35\sqrt{30090}}{2}\times \frac{1}{100000000\sqrt{10}}$$

Rationalize the denominator of \frac{1}{100000000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{35\sqrt{30090}}{2}\times \frac{\sqrt{10}}{100000000\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{35\sqrt{30090}}{2}\times \frac{\sqrt{10}}{100000000\times 10}$$

Multiply 100000000 and 10 to get 1000000000.

$$\frac{35\sqrt{30090}}{2}\times \frac{\sqrt{10}}{1000000000}$$

Multiply \frac{35\sqrt{30090}}{2} times \frac{\sqrt{10}}{1000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\sqrt{30090}\sqrt{10}}{2\times 1000000000}$$

Cancel out 5 in both numerator and denominator.

$$\frac{7\sqrt{10}\sqrt{30090}}{2\times 200000000}$$

Factor 30090=10\times 3009. Rewrite the square root of the product \sqrt{10\times 3009} as the product of square roots \sqrt{10}\sqrt{3009}.

$$\frac{7\sqrt{10}\sqrt{10}\sqrt{3009}}{2\times 200000000}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$\frac{7\times 10\sqrt{3009}}{2\times 200000000}$$

Multiply 7 and 10 to get 70.

$$\frac{70\sqrt{3009}}{2\times 200000000}$$

Multiply 2 and 200000000 to get 400000000.

$$\frac{70\sqrt{3009}}{400000000}$$

Divide 70\sqrt{3009} by 400000000 to get \frac{7}{40000000}\sqrt{3009}.

$$\frac{7}{40000000}\sqrt{3009}$$