Solve =sqrt{0.5/50*10^3}

$$= \sqrt { \frac { 0.5 } { 50 \times 10 ^ { 3 } } }$$

Evaluate

$$\frac{\sqrt{10}}{1000}\approx 0.003162278$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$\sqrt{\frac{0.5}{50\times 1000}}$$

Multiply 50 and 1000 to get 50000.

$$\sqrt{\frac{0.5}{50000}}$$

Expand \frac{0.5}{50000} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{5}{500000}}$$

Reduce the fraction \frac{5}{500000} to lowest terms by extracting and canceling out 5.

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

Rewrite the square root of the division \sqrt{\frac{1}{100000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{100000}}.

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

Calculate the square root of 1 and get 1.

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

Factor 100000=100^{2}\times 10. Rewrite the square root of the product \sqrt{100^{2}\times 10} as the product of square roots \sqrt{100^{2}}\sqrt{10}. Take the square root of 100^{2}.

$$\frac{1}{100\sqrt{10}}$$

Rationalize the denominator of \frac{1}{100\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{10}}{100\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{10}}{100\times 10}$$

Multiply 100 and 10 to get 1000.

$$\frac{\sqrt{10}}{1000}$$