Question

In the following exercises, simplify.

$\frac{5+\sqrt{125}}{15}$

Short answer

The simplified expression is$\frac{1+\sqrt{5}}{3}$

Step-by-step solution

Given information

We are given a expression$\frac{5+\sqrt{125}}{15}$

Simplify the radical

We have,

$$\begin{gathered} \frac{5+\sqrt{125}}{15} \\ =\frac{5+\sqrt{25}·\sqrt{5}}{15} \\ =\frac{5+5\sqrt{5}}{15} \end{gathered}$$

Cancel the common factor and simplify

We get,

$$\begin{gathered} \frac{5+5\sqrt{5}}{15} \\ =\frac{5(1+\sqrt{5})}{15} \\ =\frac{1+\sqrt{5}}{3} \end{gathered}$$

Conclusion

The simplified expression is$\frac{1+\sqrt{5}}{3}$