Solve sqrt{9*10^-6*10^-8/9*10^-3}

$$\sqrt{ \frac{ 9 \times { 10 }^{ -6 } \times { 10 }^{ -8 } }{ 9 \times { 10 }^{ -3 } } }$$

Evaluate

$$\frac{\sqrt{10}}{1000000}\approx 0.000003162$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and -8 to get -14.

$$\sqrt{\frac{9\times 10^{-14}}{9\times 10^{-3}}}$$

Cancel out 9 in both numerator and denominator.

$$\sqrt{\frac{10^{-14}}{10^{-3}}}$$

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

$$\sqrt{\frac{1}{10^{11}}}$$

Calculate 10 to the power of 11 and get 100000000000.

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

Rewrite the square root of the division \sqrt{\frac{1}{100000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{100000000000}}.

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

Calculate the square root of 1 and get 1.

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

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}.

$$\frac{1}{100000\sqrt{10}}$$

Rationalize the denominator of \frac{1}{100000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

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

The square of \sqrt{10} is 10.

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

Multiply 100000 and 10 to get 1000000.

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