Solve frac{1+sqrt{5}}{sqrt{3}}

$$\frac { 1 + \sqrt { 5 } } { \sqrt { 3 } }$$

Evaluate

$$\frac{\sqrt{3}\left(\sqrt{5}+1\right)}{3}\approx 1.868344718$$

Solution Steps

Rationalize the denominator of \frac{1+\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(1+\sqrt{5}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(1+\sqrt{5}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 1+\sqrt{5} by \sqrt{3}.

$$\frac{\sqrt{3}+\sqrt{5}\sqrt{3}}{3}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{3}+\sqrt{15}}{3}$$