# 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: Simplify 7/(2√(3))

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:

7/(2√(3))*√(3)/√(3)=7√(3)/(2√(3)√(3))

Above, we have multiplied 7/(2√(3)), top and bottom, by √(3). 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 √(3)√(3)=3. Therefore,

7/(2√(3))*√(3)/√(3)=7√(3)/(2√(3)√(3))=7√(3)/(2*3)=7√(3)/6

So it turns out that, when you rationalize the denominator,7/(2√(3)) becomes 7√(3)/6

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.