The document discusses rationalizing the denominator of a radical expression. Rationalizing means finding an equivalent expression where the denominator is a perfect square by multiplying the numerator and denominator by the radical in the denominator. This removes the radical from the denominator and makes the expression rational. For example, to rationalize 3/√3, we multiply the numerator and denominator by √3, giving (3√3)/(3) = 1.

1. OBJECTIVE
•Rationalize the denominator
of a radical expression.

2. Rationalizing the denominator
•means to find a radical expression
which when we multiplied to both
numerator and denominator will
make the denominator a perfect
square which then simplifies to a
rational expression.

3. •A radical is not considered simplified if
there is a radical sign in the
denominator.
•To remove the radical sign is to
rationalize.
•The process of eliminating the radicals
in the denominator is called
rationalization.

4. 6
3
2
6

5. There is an agreement
3
1
in mathematics
that we don’t leave a radical
in the denominator
of a fraction.

6. So how do we change the
denominator of a fraction?
3
1
(Without changing the value of
the fraction, of course.)

7. By what number
to a rational number?
to change it
3
1
3
can we multiply

8. The answer is . . .
3
1
3
. . . by itself!
 3   23 3

9. In our fraction, to get the radical
out of the denominator,
we can multiply numerator and
denominator by .3
3
1

10. 
3
1

33
31
3
3
In our fraction, to get the radical
out of the denominator,
we can multiply numerator and
denominator by .3

11. 
3
1
3
3
Because we are changing
the denominator
we call this process
rationalizing.
to a rational number,

12. 
2
4

22
24
Rationalize the denominator:

2
24
22
2

13. 
12
64

12
8

1212
128
Rationalize the denominator:
3
6
3

12
96

14. Rationalize the following:
•