Solve sqrt{5.61*10^-12/0.0010}

$$\sqrt { \frac { 5.61 \times 10 ^ { - 12 } } { 0.0010 } }$$

Evaluate

$$\frac{\sqrt{5610}}{1000000}\approx 0.0000749$$

Solution Steps

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$\sqrt{\frac{5.61\times \frac{1}{1000000000000}}{0.001}}$$

Multiply 5.61 and \frac{1}{1000000000000} to get \frac{561}{100000000000000}.

$$\sqrt{\frac{\frac{561}{100000000000000}}{0.001}}$$

Express \frac{\frac{561}{100000000000000}}{0.001} as a single fraction.

$$\sqrt{\frac{561}{100000000000000\times 0.001}}$$

Multiply 100000000000000 and 0.001 to get 100000000000.

$$\sqrt{\frac{561}{100000000000}}$$

Rewrite the square root of the division \sqrt{\frac{561}{100000000000}} as the division of square roots \frac{\sqrt{561}}{\sqrt{100000000000}}.

$$\frac{\sqrt{561}}{\sqrt{100000000000}}$$

Factor 100000000000=100000^{2}\times 10. Rewrite the square root of the product \sqrt{100000^{2}\times 10} as the product of square roots \sqrt{100000^{2}}\sqrt{10}. Take the square root of 100000^{2}.

$$\frac{\sqrt{561}}{100000\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{561}}{100000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{561}\sqrt{10}}{100000\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{561}\sqrt{10}}{100000\times 10}$$

To multiply \sqrt{561} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{5610}}{100000\times 10}$$

Multiply 100000 and 10 to get 1000000.

$$\frac{\sqrt{5610}}{1000000}$$