Download Roots of Real Numbers and Radical Expressions Part 2

Simplifying Radical
Expressions
• Basic multiplication
• Basic division
o Rationalize the denominator
Product Property of
Radicals
For any numbers a and
b where a 0and b 0,
ab  a  b
Examples:
Quotient Property of
Radicals
For any numbers a and
b where a 0and b 0,
a

b
a
b
Examples:
5
3
What if the
denominator still has
a radical???????
Rationalizing the
denominator
Rationalizing the denominator means
to remove any radicals from the
denominator.
Examples:
1.
5
4
10 8
2.
5
3.
5
2 2
Examples:
Simplifying Radical
Expressions
• Add
• Multiply
o Conjugates
Adding radicals
We can only combine terms with radicals
if we have like radicals
6 7 5 7  3 7  8 7
Multiplying radicals Distributive Property
 2  4 3
3

3 2  3 4 3

6  12
Check Yo Self!
1. 2 3 + 5 + 7 3 - 2
2. 5 6  3 24  150
3.
2
34 5
4.
5
4 2 7

 5
3 6 5

4 2 7

5 6
3 2
How do we rationalize
a denominator like
this???????
Conjugates
5  6  Conjugate:
5 6
3  2 2  Conjugate: 3  2 2
The product of conjugates is a rational
number. Therefore, we can rationalize
denominator of a fraction by multiplying by
its conjugate.
2 6
3 2
Check Yo Self!
1.
32
3 5
1 2 5
2.
6 5