Solve sqrt{3.7*10^-9/9*10^9}

$$\sqrt { \frac { 3.7 \times 10 ^ { - 9 } } { 9 \times 10 ^ { 9 } } }$$

Evaluate

$$\frac{\sqrt{370}}{30000000000}\approx 6.411794687 \cdot 10^{-10}$$

Solution Steps

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

$$\sqrt{\frac{3.7}{9\times 10^{18}}}$$

Calculate 10 to the power of 18 and get 1000000000000000000.

$$\sqrt{\frac{3.7}{9\times 1000000000000000000}}$$

Multiply 9 and 1000000000000000000 to get 9000000000000000000.

$$\sqrt{\frac{3.7}{9000000000000000000}}$$

Expand \frac{3.7}{9000000000000000000} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{37}{90000000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{37}{90000000000000000000}} as the division of square roots \frac{\sqrt{37}}{\sqrt{90000000000000000000}}.

$$\frac{\sqrt{37}}{\sqrt{90000000000000000000}}$$

Factor 90000000000000000000=3000000000^{2}\times 10. Rewrite the square root of the product \sqrt{3000000000^{2}\times 10} as the product of square roots \sqrt{3000000000^{2}}\sqrt{10}. Take the square root of 3000000000^{2}.

$$\frac{\sqrt{37}}{3000000000\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{37}}{3000000000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{37}\sqrt{10}}{3000000000\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{37}\sqrt{10}}{3000000000\times 10}$$

To multiply \sqrt{37} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{370}}{3000000000\times 10}$$

Multiply 3000000000 and 10 to get 30000000000.

$$\frac{\sqrt{370}}{30000000000}$$