Solve (sqrt{5}-x)divsqrt{2}

$$( \sqrt { 5 } - x ) \div \sqrt { 2 }$$

Evaluate

$$\frac{\sqrt{2}\left(-x+\sqrt{5}\right)}{2}$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Use the distributive property to multiply \sqrt{5}-x by \sqrt{2}.

$$\frac{\sqrt{5}\sqrt{2}-x\sqrt{2}}{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{10}-x\sqrt{2}}{2}$$

Differentiate w.r.t. x

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