Solve sqrt{6369*10^-7}

$$\sqrt { 6369 \times 10 ^ { - 7 } }$$

Evaluate

$$\frac{\sqrt{63690}}{10000}\approx 0.025236878$$

Solution Steps

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\sqrt{6369\times \frac{1}{10000000}}$$

Multiply 6369 and \frac{1}{10000000} to get \frac{6369}{10000000}.

$$\sqrt{\frac{6369}{10000000}}$$

Rewrite the square root of the division \sqrt{\frac{6369}{10000000}} as the division of square roots \frac{\sqrt{6369}}{\sqrt{10000000}}.

$$\frac{\sqrt{6369}}{\sqrt{10000000}}$$

Factor 10000000=1000^{2}\times 10. Rewrite the square root of the product \sqrt{1000^{2}\times 10} as the product of square roots \sqrt{1000^{2}}\sqrt{10}. Take the square root of 1000^{2}.

$$\frac{\sqrt{6369}}{1000\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{6369}}{1000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{6369}\sqrt{10}}{1000\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{6369}\sqrt{10}}{1000\times 10}$$

To multiply \sqrt{6369} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{63690}}{1000\times 10}$$

Multiply 1000 and 10 to get 10000.

$$\frac{\sqrt{63690}}{10000}$$