Solve 2v1/6sqrt{12}

$$\frac { 2 v 1 } { 6 \sqrt { 12 } }$$

Evaluate

$$\frac{\sqrt{3}v_{1}}{18}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{v_{1}}{3\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{v_{1}}{3\times 2\sqrt{3}}$$

Multiply 3 and 2 to get 6.

$$\frac{v_{1}}{6\sqrt{3}}$$

Rationalize the denominator of \frac{v_{1}}{6\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{v_{1}\sqrt{3}}{6\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{v_{1}\sqrt{3}}{6\times 3}$$

Multiply 6 and 3 to get 18.

$$\frac{v_{1}\sqrt{3}}{18}$$

Differentiate w.r.t. v_1

$$\frac{\sqrt{3}}{18} = 0.09622504486493762$$