Simplifying Radical Expressions

• Basic multiplication• Basic divisiono Rationalize the denominator

Product Property of Radicals

For any numbers a and b where and , a0

ab a b

b0

Examples:

Quotient Property of Radicals

For any numbers a and b where and , a0 b0

ab

a

b

Examples:

What if the denominator still has a radical???????

5

3

Rationalizing the denominator

Rationalizing the denominator means to remove any radicals from the denominator.

Examples:5

1. 4

10 82.

5

3.

5

2 2

Examples:

Simplifying Radical Expressions

• Add• Multiplyo Conjugates

Adding radicals

6 7 5 7 3 7

We can only combine terms with radicals if we have like radicals

8 7

Multiplying radicals - Distributive Property

3 24 3

3 2 34 3

612

Check Yo Self!

1. 2 3 + 5 + 7 3 - 2

2. 5 6 3 24 150

3. 2 3 4 5 3 6 5

4. 5 4 2 7 5 4 2 7

How do we rationalize a denominator like this???????

5 6

3 2

Conjugates

The product of conjugates is a rational number. Therefore, we can rationalize

denominator of a fraction by multiplying by its conjugate.

5 6 Conjugate: 5 6

3 2 2 Conjugate: 3 2 2

2 6

3 2

3 21.

3 5

1 2 52.

6 5

Check Yo Self!