Simplifying Radicals
Product Rule for Radicals:
 The product rule for radicals states that the product of two
square roots is equal to the square root of the product.
Example 1:
√
√
√
√
We can evaluate this way:
√
√
And we get the same answer.
We will use the product rule for radicals to simplify radical
expressions.
Example 2:
Simplify √ .
√
√
√
√
√
√
1
Example 3:
Simplify √
√
.
can be broken down in two ways:
√
√
Since
√
√
OR
√
is a perfect square, we choose to break up √
√
√
√
√
Example 4:
Simplify √
.
We want to write
√
as a product.
√
√
√
√
√
√
√
√
2
√
Perfect Cubes:
is a perfect cube since
Written in math:
√
said “the cube root of
is ”.
Example 5:
Evaluate:
a.) √
b.) √
c.) √
d.) √
3
Simplify Radicals
Practice Problems
Simplify:
1. √
2. √
3. √
Evaluate:
4. √
5. √
4