Solve sqrt{2.3*10^-9/0.1}

$$\sqrt{ \frac{ 2.3 \times { 10 }^{ -9 } }{ 0.1 } }$$

Evaluate

$$\frac{\sqrt{230}}{100000}\approx 0.000151658$$

Solution Steps

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\sqrt{\frac{2.3\times \frac{1}{1000000000}}{0.1}}$$

Multiply 2.3 and \frac{1}{1000000000} to get \frac{23}{10000000000}.

$$\sqrt{\frac{\frac{23}{10000000000}}{0.1}}$$

Express \frac{\frac{23}{10000000000}}{0.1} as a single fraction.

$$\sqrt{\frac{23}{10000000000\times 0.1}}$$

Multiply 10000000000 and 0.1 to get 1000000000.

$$\sqrt{\frac{23}{1000000000}}$$

Rewrite the square root of the division \sqrt{\frac{23}{1000000000}} as the division of square roots \frac{\sqrt{23}}{\sqrt{1000000000}}.

$$\frac{\sqrt{23}}{\sqrt{1000000000}}$$

Factor 1000000000=10000^{2}\times 10. Rewrite the square root of the product \sqrt{10000^{2}\times 10} as the product of square roots \sqrt{10000^{2}}\sqrt{10}. Take the square root of 10000^{2}.

$$\frac{\sqrt{23}}{10000\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{23}}{10000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{23}\sqrt{10}}{10000\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{23}\sqrt{10}}{10000\times 10}$$

To multiply \sqrt{23} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{230}}{10000\times 10}$$

Multiply 10000 and 10 to get 100000.

$$\frac{\sqrt{230}}{100000}$$