Solve sqrt{3.2*10^-13/0.1}

$$\sqrt{ \frac{ 3.2 \times { 10 }^{ -13 } }{ 0.1 } }$$

Evaluate

$$\frac{\sqrt{5}}{1250000}\approx 0.000001789$$

Solution Steps

Calculate 10 to the power of -13 and get \frac{1}{10000000000000}.

$$\sqrt{\frac{3.2\times \frac{1}{10000000000000}}{0.1}}$$

Multiply 3.2 and \frac{1}{10000000000000} to get \frac{1}{3125000000000}.

$$\sqrt{\frac{\frac{1}{3125000000000}}{0.1}}$$

Express \frac{\frac{1}{3125000000000}}{0.1} as a single fraction.

$$\sqrt{\frac{1}{3125000000000\times 0.1}}$$

Multiply 3125000000000 and 0.1 to get 312500000000.

$$\sqrt{\frac{1}{312500000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{312500000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{312500000000}}.

$$\frac{\sqrt{1}}{\sqrt{312500000000}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{312500000000}}$$

Factor 312500000000=250000^{2}\times 5. Rewrite the square root of the product \sqrt{250000^{2}\times 5} as the product of square roots \sqrt{250000^{2}}\sqrt{5}. Take the square root of 250000^{2}.

$$\frac{1}{250000\sqrt{5}}$$

Rationalize the denominator of \frac{1}{250000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{250000\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{250000\times 5}$$

Multiply 250000 and 5 to get 1250000.

$$\frac{\sqrt{5}}{1250000}$$