Solve sqrt{0,1/2}

$$\sqrt { \frac { 0,1 } { 2 } }$$

Evaluate

$$\frac{\sqrt{5}}{10}\approx 0.223606798$$

Solution Steps

Expand \frac{0,1}{2} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{1}{20}}$$

Rewrite the square root of the division \sqrt{\frac{1}{20}} as the division of square roots \frac{\sqrt{1}}{\sqrt{20}}.

$$\frac{\sqrt{1}}{\sqrt{20}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{1}{2\sqrt{5}}$$

Rationalize the denominator of \frac{1}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{\sqrt{5}}{10}$$