Solve sqrt{10^-4/(1*8)^2}

$$\sqrt { \frac { 10 ^ { - 4 } } { ( 1 \cdot 8 ) ^ { 2 } } }$$

Evaluate

$$\frac{1}{800}=0.00125$$

Solution Steps

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\sqrt{\frac{\frac{1}{10000}}{\left(1\times 8\right)^{2}}}$$

Multiply 1 and 8 to get 8.

$$\sqrt{\frac{\frac{1}{10000}}{8^{2}}}$$

Calculate 8 to the power of 2 and get 64.

$$\sqrt{\frac{\frac{1}{10000}}{64}}$$

Express \frac{\frac{1}{10000}}{64} as a single fraction.

$$\sqrt{\frac{1}{10000\times 64}}$$

Multiply 10000 and 64 to get 640000.

$$\sqrt{\frac{1}{640000}}$$

Rewrite the square root of the division \frac{1}{640000} as the division of square roots \frac{\sqrt{1}}{\sqrt{640000}}. Take the square root of both numerator and denominator.

$$\frac{1}{800}$$

Factor

$$\frac{1}{2 ^ {5} \cdot 5 ^ {2}} = 0.00125$$