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

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

Evaluate

$$\frac{\sqrt{2}}{3}+3\sqrt{5}\approx 7.179608453$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3\sqrt{5} times \frac{3}{3}.

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

Since \frac{\sqrt{2}}{3} and \frac{3\times 3\sqrt{5}}{3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \sqrt{2}+3\times 3\sqrt{5}.

$$\frac{\sqrt{2}+9\sqrt{5}}{3}$$

Factor

$$\frac{\sqrt{2} + 9 \sqrt{5}}{3} = 7.179608453290402$$