Solve sqrt{9*10^-5*16/8*5}

$$\sqrt{ \frac{ 9 \times { 10 }^{ -5 } \times 16 }{ 8 \times 5 } }$$

Evaluate

$$\frac{3}{500}=0.006$$

Solution Steps

Cancel out 8 in both numerator and denominator.

$$\sqrt{\frac{2\times 9\times 10^{-5}}{5}}$$

Multiply 2 and 9 to get 18.

$$\sqrt{\frac{18\times 10^{-5}}{5}}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\sqrt{\frac{18\times \frac{1}{100000}}{5}}$$

Multiply 18 and \frac{1}{100000} to get \frac{9}{50000}.

$$\sqrt{\frac{\frac{9}{50000}}{5}}$$

Express \frac{\frac{9}{50000}}{5} as a single fraction.

$$\sqrt{\frac{9}{50000\times 5}}$$

Multiply 50000 and 5 to get 250000.

$$\sqrt{\frac{9}{250000}}$$

Rewrite the square root of the division \frac{9}{250000} as the division of square roots \frac{\sqrt{9}}{\sqrt{250000}}. Take the square root of both numerator and denominator.

$$\frac{3}{500}$$

Factor

$$\frac{3}{2 ^ {2} \cdot 5 ^ {3}} = 0.006$$