9. FOIL with Radicals
• Use rules for multiplying and add/subtract
• Ex: (3 + 5)( 5 − 4)
10.
11. To divide radicals:
divide the coefficients,
divide the radicands if
possible, and
rationalize the
denominator so that
no radical remains in
the denominator
13.
7
6
This cannot be
divided which leaves
the radical in the
denominator. We do
not leave radicals in
the denominator. So
we need to
rationalize by
multiplying the
fraction by something
so we can eliminate
the radical in the
denominator.
7
7
*
7
6
49
42
7
42
42 cannot be
simplified, so we are
finished.
Example 2:
14. This can be divided
which leaves the
radical in the
denominator. We do
not leave radicals in
the denominator. So
we need to
rationalize by
multiplying the
fraction by something
so we can eliminate
the radical in the
denominator.
10
5
2
2
*
2
1
2
2
Example 3:
15. This cannot be
divided which leaves
the radical in the
denominator. We do
not leave radicals in
the denominator. So
we need to
rationalize by
multiplying the
fraction by something
so we can eliminate
the radical in the
denominator.
12
3
3
3
*
32
3
9*2
33
6
33
2
3Reduce
the
fraction.
Example 4: