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

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

Evaluate

$$\frac{\sqrt{15}}{3}+1\approx 2.290994449$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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

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

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

$$\frac{\sqrt{15}+\left(\sqrt{3}\right)^{2}}{3}$$

The square of \sqrt{3} is 3.

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