Download Nth Roots

Objective: Students will be able to simplify radicals
Key Concept – for any real numbers a and b, and any positive integer n, if a n=b
then a is the n th root of b.
For example:
 62=36, so 6 is the square root of 36
 25=32, so 2 is the fifth root of 32
 43=64. so 4 is the cube root of 64
The symbol
n
indicates an n th root.
5
radicand
243
index
Another way of interpreting this is to ask yourself, “What number to the 5 th
power is equal to 243?”
So____________ is the 5th root of 243.
Here is a helpful chart to help us determine how many and what type of roots
we are solving for.
n
n
b if b>0
n
b if b<0
EVEN
One positive root,
one negative root
No real roots
ODD
One positive root
One negative root
n
b if b=0
One real root, 0
When there is more than one real root, the non-negative root is called the
principal root.
Let’s stop and check for understanding. Complete the following examples.
1.
16 
2.
3
125 
3.
4
 16
4.
7
1
For your reference:
12 
13 
14 
15 
22 
23 
24 
25 
32 
33 
34 
35 
42 
43 
44 
45 
52 
53 
54 
55 
This idea can be expanded to perfect powers of a variable in the radicand. The
radicand xn
is a perfect power when
 n is a multiple of
 the index. A quick way to
do this is to figure out if the exponent is divisible by the index.

5.
8
6.
25x 4
7.
5
 32 x15 y 20
8.
4
( x  4) 8
9.
10.

x8
x 2  8x 16
3
27 x 3 y 9