Solve sqrt{2*2*10^-2/2.11*10^16}

$$\sqrt { \frac { 2 \times 2 \times 10 ^ { - 2 } } { 2.11 \times 10 ^ { 16 } } }$$

Evaluate

$$\frac{\sqrt{211}}{10550000000}\approx 1.376856782 \cdot 10^{-9}$$

Solution Steps

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

$$\sqrt{\frac{2\times 2}{2.11\times 10^{18}}}$$

Multiply 2 and 2 to get 4.

$$\sqrt{\frac{4}{2.11\times 10^{18}}}$$

Calculate 10 to the power of 18 and get 1000000000000000000.

$$\sqrt{\frac{4}{2.11\times 1000000000000000000}}$$

Multiply 2.11 and 1000000000000000000 to get 2110000000000000000.

$$\sqrt{\frac{4}{2110000000000000000}}$$

Reduce the fraction \frac{4}{2110000000000000000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{1}{527500000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{527500000000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{527500000000000000}}.

$$\frac{\sqrt{1}}{\sqrt{527500000000000000}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{527500000000000000}}$$

Factor 527500000000000000=50000000^{2}\times 211. Rewrite the square root of the product \sqrt{50000000^{2}\times 211} as the product of square roots \sqrt{50000000^{2}}\sqrt{211}. Take the square root of 50000000^{2}.

$$\frac{1}{50000000\sqrt{211}}$$

Rationalize the denominator of \frac{1}{50000000\sqrt{211}} by multiplying numerator and denominator by \sqrt{211}.

$$\frac{\sqrt{211}}{50000000\left(\sqrt{211}\right)^{2}}$$

The square of \sqrt{211} is 211.

$$\frac{\sqrt{211}}{50000000\times 211}$$

Multiply 50000000 and 211 to get 10550000000.

$$\frac{\sqrt{211}}{10550000000}$$