Solve frac{4+3sqrt{5}}{sqrt{3}}

$$\frac { 4 + 3 \sqrt { 5 } } { \sqrt { 3 } }$$

Evaluate

$$\frac{4\sqrt{3}}{3}+\sqrt{15}\approx 6.182384423$$

Solution Steps

Rationalize the denominator of \frac{4+3\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(4+3\sqrt{5}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(4+3\sqrt{5}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 4+3\sqrt{5} by \sqrt{3}.

$$\frac{4\sqrt{3}+3\sqrt{5}\sqrt{3}}{3}$$

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

$$\frac{4\sqrt{3}+3\sqrt{15}}{3}$$