Date: 4-10/11-12
Topic: 6-3 Sums of
Radicals
Objective
Definition:
Essential Question: Under what conditions can you add and
subtract radicals, and what is the process?
The student will learn to simplify expressions involving sums
of radicals.
Two radicals with the same index and radicand are called like
radicals.
You can apply the distributive property to add or subtract like
radicals in the same way as like terms.
Like
Radicals:
√
and
√
are like radicals, because they have the same radicand and the
same index.
√
and
√
are not like radicals, because they have different radicands.
√
and
√
are not like radicals, because they have different indices.
Summary
1
Combining like
terms
In ordinary algebra, you can Combine like terms.
Use the distributive property to simplify the following
expression by combining like terms:
(
)
x and y are not like terms, and they cannot be combined.
Use the distributive property to simplify the following
expression by combining like radicals:
√
√
√
√
( √
√ )
√
√
√ and √ are not like radicals, and they cannot be combined
Using Like Radicals
Sometimes you can transform unlike radicals and then simplify
the radical expression.
√
Simplify
√
√
√
√
√
√
√
√
Exercise:
Simplify
√
√
2
Using Like Radicals:
Look for factors in each radical that are perfect powers of the
index.
√
Simplify
√
√
√
√
√
√
√
√
Exercise:
Simplify
√
√
Remember, the index must always be the same.
Simplify
√
√
Not possible: the indices are different.
3
Using Like Radicals:
√
Simplify
√
√
√
√
√
√
√
√
√
√
√
Exercise:
Simplify
√
√
√
√
√
√
√
4
Using Like Radicals:
Use the distributive property to transform unlike radicals and
then simplify the radical expression.
√ (√
Simplify
√
√
√
√
Exercise:
Simplify
√
√
√ )
√
√
√
√
√ (√
√ )
5
Using Like Radicals:
The distributive property also applies to quotients.
√
√
Simplify
√
√
√
√
Exercise:
Simplify
√
√
√
√
√
√
√
√
√
√
√
6
Assume that each radical represents a real number.
Example:
√
Simplify
√
√
√
√
√
√
√
√
Answer:
Exercise:
√
Assume that each radical represents a real number.
Simplify
√
√
7
Assume that each radical represents a real number.
Example:
√
√
√
√
√
√
√
√
√
Answer:
Exercise:
√
√
Simplify
Assume that each radical represents a real number.
Simplify
√
√
√
√
8