Solve xsqrt{1/5}

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

Evaluate

$$\frac{\sqrt{5}x}{5}$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$x\times \frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$x\times \frac{1}{\sqrt{5}}$$

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

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

The square of \sqrt{5} is 5.

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

Express x\times \frac{\sqrt{5}}{5} as a single fraction.

$$\frac{x\sqrt{5}}{5}$$

Differentiate w.r.t. x

$$\frac{\sqrt{5}}{5} = 0.447213595499958$$