Solve sqrt{2*2*10^-4/2.11*10^-12}

$$\sqrt { \frac { 2 \times 2 \times 10 ^ { - 4 } } { 2.11 \times 10 ^ { - 12 } } }$$

Evaluate

$$\frac{200000\sqrt{211}}{211}\approx 13768.56781643$$

Solution Steps

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

$$\sqrt{\frac{2\times 2\times 10^{8}}{2.11}}$$

Multiply 2 and 2 to get 4.

$$\sqrt{\frac{4\times 10^{8}}{2.11}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\sqrt{\frac{4\times 100000000}{2.11}}$$

Multiply 4 and 100000000 to get 400000000.

$$\sqrt{\frac{400000000}{2.11}}$$

Expand \frac{400000000}{2.11} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{40000000000}{211}}$$

Rewrite the square root of the division \sqrt{\frac{40000000000}{211}} as the division of square roots \frac{\sqrt{40000000000}}{\sqrt{211}}.

$$\frac{\sqrt{40000000000}}{\sqrt{211}}$$

Calculate the square root of 40000000000 and get 200000.

$$\frac{200000}{\sqrt{211}}$$

Rationalize the denominator of \frac{200000}{\sqrt{211}} by multiplying numerator and denominator by \sqrt{211}.

$$\frac{200000\sqrt{211}}{\left(\sqrt{211}\right)^{2}}$$

The square of \sqrt{211} is 211.

$$\frac{200000\sqrt{211}}{211}$$