11.1
Simplifying Radicals
11.1 – Simplifying Radicals
Goals / “I can…”
Simplify radicals involving products
Simplify radicals involving quotients
11.1 – Simplifying Radicals
A radical expression has a square root
(radical).
11.1 – Simplifying Radicals
NOT something radical!!!!
11.1 – Simplifying Radicals
Write down as many perfect squares as
you can remember.
Remembering these will help with
today’s problems.
36
81
144
49
Perfect Squares
1
64
225
4
81
256
9
16
100
121
289
25
36
49
144
169
196
400
324
625
11.1 – Simplifying Radicals
4
=2
16
=4
25
=5
100
= 10
144
= 12
11.1 – Simplifying Radicals
But what if the number under the
square root is not perfect?
11.1 – Simplifying Radicals
Using the Multiplicative Property of
Square Roots will help.
For every number, a ⋅ b = a b
11.1 – Simplifying Radicals
Example:
72
Is there a perfect square in the number?
36 ⋅ 2
36
6 2
2
11.1 – Simplifying Radicals
Does it work with variables?
a7
Is there a way of breaking down the 7?
6 1
aa
a6
a1
a 3 a1
11.1 – Simplifying Radicals
TRY:
28x
5
60a
8
3 10
x y
11.1 – Simplifying Radicals
Can you multiply radicals?
8a
12a
96a
2
Solve this like the others.
11.1 – Simplifying Radicals
Dividing radicals
a
b
=
a
b
11.1 – Simplifying Radicals
Example:
144
144 12
=
=
121
121 11
11.1 – Simplifying Radicals
Rationalizing the denominator
We CANNOT have a radical in the
denominator.
11.1 – Simplifying Radicals
If we have a problem like the following:
4
6
Multiply the top and bottom by
4
6 4 6 4 6 2 6
⋅
=
=
=
6
3
6 6
36
6
11.1 – Simplifying Radicals
TRY:
5
6
11.1 – Simplifying Radicals
TRY:
7
7