Solve sqrt{10^-92/30}

$$\sqrt{ { 10 }^{ -9 } \frac{ 2 }{ 30 } }$$

Evaluate

$$\frac{\sqrt{6}}{300000}\approx 0.000008165$$

Solution Steps

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

$$\sqrt{\frac{1}{1000000000}\times \frac{2}{30}}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1}{1000000000}\times \frac{1}{15}}$$

Multiply \frac{1}{1000000000} and \frac{1}{15} to get \frac{1}{15000000000}.

$$\sqrt{\frac{1}{15000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{15000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{15000000000}}.

$$\frac{\sqrt{1}}{\sqrt{15000000000}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{15000000000}}$$

Factor 15000000000=50000^{2}\times 6. Rewrite the square root of the product \sqrt{50000^{2}\times 6} as the product of square roots \sqrt{50000^{2}}\sqrt{6}. Take the square root of 50000^{2}.

$$\frac{1}{50000\sqrt{6}}$$

Rationalize the denominator of \frac{1}{50000\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{6}}{50000\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{6}}{50000\times 6}$$

Multiply 50000 and 6 to get 300000.

$$\frac{\sqrt{6}}{300000}$$