Warm Up
4/25/17
Simplify
1. √27
2. √75
3. 7√28
4. 2√125
Rationalizing the denominator
Rationalizing the denominator simply means removing all radicals
from the denominator of the fraction without changing the value of
the fraction. This puts the fraction in simplest form and makes it
easier to understand and compare with other fractions.
To rationalize the denominator:
3
√2
1. Multiply the numerator and denominator by the same radical
that is in the denominator (you are just multiplying by 1 so it
doesn’t change the problem)
3
⋅
√2
√2 √2
2. Simplify. Sometimes you will also have to reduce or simplify
the radical.
3√2 3√2
=
2
√4
Try:
2.
1.
6
√3
3
√5
3.
12
6√3
Make sure when you rationalize the denominator that the
denominator is simplified before you start.
Example: Rationalize
5
√12
√12 can be simplified. √12 = √4 ⋅ 3 = 2√3
Write the problem with the simplified radical.
5
Continue to rationalize.
2√3
=
⋅
5√3
2√9
=
=
5√3
2⋅3
5√3
6
√3
√3
5
2√3