Solve frac{1+sqrt{3}y}{sqrt{3}}

$$\frac{ 1+ \sqrt{ 3 } y }{ \sqrt{ 3 } }$$

Evaluate

$$y = \frac{\sqrt{3}}{3} = 0.5773502691896257$$

Solution Steps

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

$$\frac{\left(1+\sqrt{3}y\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(1+\sqrt{3}y\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 1+\sqrt{3}y by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}+y\times 3}{3}$$

Differentiate w.r.t. y

$$1$$