Solve v^2/sqrt{frac{1{2}}}

$$\frac { v ^ { 2 } } { \sqrt { \frac { 1 } { 2 } } }$$

Evaluate

$$\sqrt{2}v^{2}$$

Solution Steps

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

$$\frac{v^{2}}{\frac{\sqrt{1}}{\sqrt{2}}}$$

Calculate the square root of 1 and get 1.

$$\frac{v^{2}}{\frac{1}{\sqrt{2}}}$$

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

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

The square of \sqrt{2} is 2.

$$\frac{v^{2}}{\frac{\sqrt{2}}{2}}$$

Divide v^{2} by \frac{\sqrt{2}}{2} by multiplying v^{2} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{v^{2}\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{v^{2}\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{v^{2}\times 2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$v^{2}\sqrt{2}$$

Differentiate w.r.t. v

$$2\sqrt{2}v$$