# Tutoring math, you cover this topic with students in late middle school or early high school.  The math tutor shows the first case.

Rationalizing the denominator is done when there’s a radical on the bottom of a fraction.  Consider the following:

Example 1:

Solution:

To rationalize the denominator, you multiply the top and bottom by the same number. The number is chosen so it turns the radical on the bottom into a whole number:

(1)

Above, we have multiplied , top and bottom, by . We can do so because when you multiply the top and bottom by the same amount, the fraction’s value doesn’t change, just its form. Notice that . Therefore,

(2)

So it turns out that, when you rationalize the denominator, becomes .

Of course, there are more complicated situations where you have to rationalize the denominator. I’ll get to them in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.