1. Simplify, Add/Sub, Mult/Div
7-4&7.5
SWBAT
Simplify radical expressions.
Add and subtract radical express.
Holt McDougal Algebra 2
Holt Algebra 2

2. In plain words…
The "nth Root" used n times in multiplication gives the original value "nth“
2nd, 3rd, 4th, 5th, ... nth ...
Instead of talking about the "4th", "16th", etc, if we want to talk generally we say the "nth“
The nth Root:
The "2nd" root is the __________________
The "3rd" root is the ___________________

3. Academic Vocab: The nth Root Notation
Radical sign
index
Radicand
When a radical sign shows no index, it represents a square root.
Reading Math

4. The nth power and its inverse
We already learned in the last section that:
and are inverses of each other.
The inverse of raising a number to the nth power is to find the nth root

5. The Principal Root
Some numbers have more than one real nth root. The non-negative root is called the principal root.
This indicates the square root of 16
This indicates the opposite of the square root of 16
This indicates both square roots of 16
This indicates the cube root of -125

6. A. sixth roots of 64
A positive number has two real sixth roots. Because 26 = 64 and (–2)6 = 64, the roots are 2 and –2.
B. cube roots of –216
A negative number has one real cube root. Because (–6)3 = –216, the root is –6.
C. fourth roots of –1024
A negative number has no real fourth roots.

7. Simplify:

8. The nth root of an even power
When we square a negative (or put it to an even power) we get a positive, therefore when taking an even root, we must make sure our answer is negative!
Simplify:

9. Think-Pair-Share

12. HOMEWORK
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#14-36 Even