Luttrell 2012
109
Name: ______________________
Date: _____
7h – Rationalizing Denominators
Dividing by radicals could require a calculator. But before those were invented, mathematicians
used a trick to get the radical out of a denominator. What’s the purpose? Dividing by a never-
ending number is quite impossible to do! But to divide by an integer is not bad at all! Even with
the invention of the calculator, most people prefer the answer to be written with the radical on in
the numerator. Mathematicians don’t consider a fraction with radicals simplified until it has
been rationalized.
The whole process of rationalizing the denominator is to multiply by one. That way the value
doesn’t change, but its appearance does. Write in
y
our own words what occurs in each step.
E
x
ample:
2
3
2
3
=
Definition of division
2
3
3
3
⋅
_______________________________
6
9
_______________________________
6
3
_______________________________
Simplif
y
:
1.
6
2
2.
3
5
3.
5
6
4.
2
6
5.
2
8
6.
4
2 3
7.
3
4 8
2
8.
2
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