Solve left(a/2sqrt{3}+a/sqrt{3}right)

$$\left( \frac{ a }{ 2 \sqrt{ 3 } } + \frac{ a }{ \sqrt{ 3 } } \right)$$

Evaluate

$$\frac{\sqrt{3}a}{2}$$

Solution Steps

Rationalize the denominator of \frac{a}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{a\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}+\frac{a}{\sqrt{3}}$$

The square of \sqrt{3} is 3.

$$\frac{a\sqrt{3}}{2\times 3}+\frac{a}{\sqrt{3}}$$

Multiply 2 and 3 to get 6.

$$\frac{a\sqrt{3}}{6}+\frac{a}{\sqrt{3}}$$

Rationalize the denominator of \frac{a}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{a\sqrt{3}}{6}+\frac{a\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{a\sqrt{3}}{6}+\frac{a\sqrt{3}}{3}$$

Combine \frac{a\sqrt{3}}{6} and \frac{a\sqrt{3}}{3} to get \frac{1}{2}a\sqrt{3}.

$$\frac{1}{2}a\sqrt{3}$$

Differentiate w.r.t. a

$$\frac{\sqrt{3}}{2} = 0.8660254037844386$$