Solve sqrt{10^-14/10^-50.05}

$$\sqrt{ \frac{ { 10 }^{ -14 } }{ { 10 }^{ -5 } } 0.05 }$$

Evaluate

$$\frac{\sqrt{2}}{200000}\approx 0.000007071$$

Solution Steps

Rewrite 10^{-5} as 10^{-14}\times 10^{9}. Cancel out 10^{-14} in both numerator and denominator.

$$\sqrt{\frac{1}{10^{9}}\times 0.05}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\sqrt{\frac{1}{1000000000}\times 0.05}$$

Multiply \frac{1}{1000000000} and 0.05 to get \frac{1}{20000000000}.

$$\sqrt{\frac{1}{20000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{20000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{20000000000}}.

$$\frac{\sqrt{1}}{\sqrt{20000000000}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{20000000000}}$$

Factor 20000000000=100000^{2}\times 2. Rewrite the square root of the product \sqrt{100000^{2}\times 2} as the product of square roots \sqrt{100000^{2}}\sqrt{2}. Take the square root of 100000^{2}.

$$\frac{1}{100000\sqrt{2}}$$

Rationalize the denominator of \frac{1}{100000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{100000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{100000\times 2}$$

Multiply 100000 and 2 to get 200000.

$$\frac{\sqrt{2}}{200000}$$