Questions: Rationalize the denominator and simplify. sqrt(11)/sqrt(7) sqrt(11)/sqrt(7)=

Transcript text: Rationalize the denominator and simplify. \[ \begin{array}{r} \frac{\sqrt{11}}{\sqrt{7}} \\ \frac{\sqrt{11}}{\sqrt{7}}= \end{array} \] $\square$

Solution

Solution Steps

To rationalize the denominator, we need to eliminate the square root in the denominator by multiplying both the numerator and the denominator by the same square root value that is in the denominator. This will result in a rational number in the denominator.

Step 1: Rationalizing the Denominator

To rationalize the denominator of the expression $ \frac{\sqrt{11}}{\sqrt{7}} $, we multiply both the numerator and the denominator by $ \sqrt{7} $:

\[ \frac{\sqrt{11}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{11} \cdot \sqrt{7}}{7} = \frac{\sqrt{77}}{7} \]

Step 2: Simplifying the Expression

The expression $ \frac{\sqrt{77}}{7} $ is already in its simplest form, as the numerator is a square root and the denominator is a rational number.