Solve 5/sqrt{20}+frac{sqrt{5}}{3}

$$\frac { 5 } { \sqrt { 20 } } + \frac { \sqrt { 5 } } { 3 }$$

Evaluate

$$\frac{5\sqrt{5}}{6}\approx 1.863389981$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{5} is 5.

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

Cancel out 5 in both numerator and denominator.

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

Combine \frac{\sqrt{5}}{2} and \frac{\sqrt{5}}{3} to get \frac{5}{6}\sqrt{5}.

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