Solve sqrt{1/6.67*10^-11}

$$\sqrt { \frac { 1 } { 6.67 \times 10 ^ { - 11 } } }$$

Evaluate

$$\frac{1000000\sqrt{6670}}{667}\approx 122443.879994575$$

Solution Steps

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\sqrt{\frac{1}{6.67\times \frac{1}{100000000000}}}$$

Multiply 6.67 and \frac{1}{100000000000} to get \frac{667}{10000000000000}.

$$\sqrt{\frac{1}{\frac{667}{10000000000000}}}$$

Divide 1 by \frac{667}{10000000000000} by multiplying 1 by the reciprocal of \frac{667}{10000000000000}.

$$\sqrt{1\times \frac{10000000000000}{667}}$$

Multiply 1 and \frac{10000000000000}{667} to get \frac{10000000000000}{667}.

$$\sqrt{\frac{10000000000000}{667}}$$

Rewrite the square root of the division \sqrt{\frac{10000000000000}{667}} as the division of square roots \frac{\sqrt{10000000000000}}{\sqrt{667}}.

$$\frac{\sqrt{10000000000000}}{\sqrt{667}}$$

Factor 10000000000000=1000000^{2}\times 10. Rewrite the square root of the product \sqrt{1000000^{2}\times 10} as the product of square roots \sqrt{1000000^{2}}\sqrt{10}. Take the square root of 1000000^{2}.

$$\frac{1000000\sqrt{10}}{\sqrt{667}}$$

Rationalize the denominator of \frac{1000000\sqrt{10}}{\sqrt{667}} by multiplying numerator and denominator by \sqrt{667}.

$$\frac{1000000\sqrt{10}\sqrt{667}}{\left(\sqrt{667}\right)^{2}}$$

The square of \sqrt{667} is 667.

$$\frac{1000000\sqrt{10}\sqrt{667}}{667}$$

To multiply \sqrt{10} and \sqrt{667}, multiply the numbers under the square root.

$$\frac{1000000\sqrt{6670}}{667}$$