Download 5.5 Roots of Real Nuumbers

5.5 Roots of Real
Numbers
Squares Roots
Nth Roots
Principal Roots
Square Roots
Since 42 = 16, then 16  4 but (-4)2 = 16.
So the square root of 16 is 4 and -4?
The Principal root is 4.
The Principal root are always positive.
Cube roots
53 = 125 , so 3 125  5
Here are the parts of a root
Square roots have index 2, which is not
shown
N th root
There are more roots then square or cubes.
If a  b, then
n
3  243;
5
5
n
b a
243  3
How do I know if the answer is
positive or negative
For example: 25  5 or  5
In case of numbers we take the principle
root “5”
When solve an equation
x2 = 25, you take the square root of
both sides. Since Square roots are even
“2”, the answer is 5 and -5
Even roots the answer have to
come out positive
Even roots
Odd roots
3
3
2
 5
 25   5  5
3
 2
 3  8  2
27  3
Other Roots
Some we will work with later in this class.
n
0 0
 16 gives you imaginery numbers
The ± symbol
± means positive and negative
So
 64 x  8x
4
2
Since x2 is positive, it does not have to be in
an absolute value
Simplify

p
3
5

4
Simplify
p


3
5
 p 5
3

2

4
Simplify
5
10 15
243a b
Simplify
5
10 15
243a b
2 3
3a b
Simplify
4
Simplify
6
a
6
Simplify
6
a
a
6
Simplify
5
243 x  2 
15
Simplify
5
243 x  2
15
3x  2
3
How do you use your Calculator to
find the values
It depends on your calculator, normal it is
function you can find with your shift button.
We will have to find it on your calculator.
Find the approximate value of
 38
3
How do you use your Calculator to
find the values
It depends on your calculator, normal it is
function you can find with your shift button.
We will have to find it on your calculator.
Find the approximate value of
 38  3.361975407  3.362
3
Homework
Page 248 – 249
#17 – 55 odd, 63
Homework
Page 248
#16 – 58 even