# What is sqrt7/sqrt11 in simplest radical form?

The simplest radical form of $\frac{\sqrt{7}}{\sqrt{11}}$ is $\frac{\sqrt{77}}{11}$.
To write this type of expression in simplest radical form, we must begin by rewriting it so that the denominator is not an irrational number. This process is called "rationalizing the denominator..' Consider $\sqrt{11}$. This is an irrational number, and to be able to replace this denominator with a rational number, it needs to be multiplied by itself. However, we can't just introduce $\sqrt{11}$ to the denominator. Therefore, we will multiply both the numerator and the denominator by $\sqrt{11}$.
$\frac{\sqrt{7}}{\sqrt{11}} \cdot \frac{\sqrt{11}}{\sqrt{11}} = \frac{\sqrt{77}}{\sqrt{121}} = \frac{\sqrt{77}}{11}$
This is the simplest radical form of $\frac{\sqrt{7}}{\sqrt{11}}$.