5-6 Radical ExpressionsObjectivesStudents will be able to:1) Simplify radical expressions2) Add, subtract, multiply, and divide radical expressions

What is a square root?• A square root is one of two equal factors of a number.

• Is that the only square root of 9?

Perfect Squares• A number that has an integer value as its square root is what is

known as a perfect square. For example, 4 is a perfect square because its square roots are 2 and -2 (both integers).• Can you name other perfect squares?

• Up to this point, we have only dealt with perfect squares as our radicands. How would we simplify a radical expression that does not have a perfect value as a radicand?

• Let’s examine the steps that could be applied to simplify square roots.

Steps to simplify a square root.1) Factor the radicand into as

many squares as possible.2) Isolate the perfect square

terms.3) Simplify each radical.

Example 2: Simplify each expression.1) 2)

3) 4)

Try these.5) 6) 7)

What about Cube Roots???

1) 2)

Now lets throw in Variables!

1) 2)

Try some more!

4) 5)

Addition/Subtraction of Square Roots• In order to add or subtract two square root expressions, the

terms must have the same radicand.• If the radicands are the same, you add/subtract the terms on

the outside of the radical expression, and keep the radicand.• You may need to simplify the terms before you can

add/subtract.

Example 3: Simplify each expression.1) 2)

3) 4)

5) 6)

Try these.7) 8)

Multiplying Radical Expressions• When multiplying radical expressions, the terms on the

outside of the radicals get multiplied, and the radicands get multiplied. You then simplify, if possible.• If you choose, you can simplify the radical expressions first (if

possible), and then multiply.• When dividing radical expressions, divide the radicands, if

possible. Again, you may choose to simplify first (if possible).

• Who wants to see some examples…

Example 4: Simplify.1) 2)

3) 4)

Try these.5) 6)

7) 8)

9)

Try these.10) 11)

Rationalize the Denominator

• There can never be a radical in the denominator of a fraction. • If a denominator contains a radical, the

expression must be rationalized. This occurs by multiplying the entire expression by a form of the number 1. The goal is to multiply by a quantity so that the radicand has an exact root.• Let’s see what this all means…

Example 5: Simplify.1) 2)

3) 4)

5) 6)

Try these.7) 8)

9)

10)

Try this.11)