Solve x/5=sqrt{1/5}

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

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{5} is 5.

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

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

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

Cancel out 5 and 5.

$$x=\sqrt{5}$$