Solve sqrt{10^-14/2*10^2}

$$\sqrt{ \frac{ { 10 }^{ -14 } }{ 2 \times { 10 }^{ 2 } } }$$

Evaluate

$$\frac{\sqrt{2}}{200000000}\approx 7.071067812 \cdot 10^{-9}$$

Solution Steps

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

$$\sqrt{\frac{1}{2\times 10^{16}}}$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\sqrt{\frac{1}{2\times 10000000000000000}}$$

Multiply 2 and 10000000000000000 to get 20000000000000000.

$$\sqrt{\frac{1}{20000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{20000000000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{20000000000000000}}.

$$\frac{\sqrt{1}}{\sqrt{20000000000000000}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{20000000000000000}}$$

Factor 20000000000000000=100000000^{2}\times 2. Rewrite the square root of the product \sqrt{100000000^{2}\times 2} as the product of square roots \sqrt{100000000^{2}}\sqrt{2}. Take the square root of 100000000^{2}.

$$\frac{1}{100000000\sqrt{2}}$$

Rationalize the denominator of \frac{1}{100000000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{100000000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{100000000\times 2}$$

Multiply 100000000 and 2 to get 200000000.

$$\frac{\sqrt{2}}{200000000}$$