Solve sqrt{1/2}x

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

Evaluate

$$\frac{\sqrt{2}x}{2}$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}x$$

Express \frac{\sqrt{2}}{2}x as a single fraction.

$$\frac{\sqrt{2}x}{2}$$

Differentiate w.r.t. x

$$\frac{\sqrt{2}}{2} = 0.7071067811865476$$