5.5 roots of real numbers and radical expressions€¦ · •5.5 simplifying radicals with...
TRANSCRIPT
Notation
814
index radical
radicand
Note: An index of 2 is understood but not
written in a square root sign.
What to do when the index will not
divide evenly into the radical????
• Smartboard Examples
• 5.5 Simplifying Radicals with
cards.notebook
Rationalizing the
denominator
5
3
Rationalizing the denominator means
to remove any radicals from the
denominator.
Ex: Simplify
5
3
3
3
5 3
9
15
3
5 3
3
Simplest Radical Form
•No perfect nth power factors
other than 1.
•No fractions in the radicand.
•No radicals in the denominator.
Adding radicals
6 7 5 73 7
6 5 3 7
We can only combine terms with radicals
if we have like radicals
8 7
Reverse of the Distributive Property
Examples:
2. 5 4 2 7 5 4 2 7
1010102 7
2 7 10 2 72 7
F O
I L
= 5 2 2 7 52 2 7
10020 7 20 7 4 49
10047 72
The product of conjugates is a
rational number. Therefore, we can
rationalize denominator of a fraction
by multiplying by its conjugate.
Ex: 5 6 Conjugate: 5 6
3 2 2 Conjugate: 3 2 2
What is conjugate of 2 7 3?
Answer: 2 7 3