Solve frac{sqrt{2}+5}{sqrt{3}}

$$\frac { \sqrt { 2 } + 5 } { \sqrt { 3 } }$$

Evaluate

$$\frac{\sqrt{3}\left(\sqrt{2}+5\right)}{3}\approx 3.703247927$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{2}+5}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Use the distributive property to multiply \sqrt{2}+5 by \sqrt{3}.

$$\frac{\sqrt{2}\sqrt{3}+5\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{6}+5\sqrt{3}}{3}$$