5.5 roots of real numbers squares roots nth roots principal roots
TRANSCRIPT
5.5 Roots of Real 5.5 Roots of Real NumbersNumbers
Squares RootsSquares Roots
Nth RootsNth Roots
Principal RootsPrincipal Roots
Square Roots
Since 42 = 16, then 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.
416
Cube roots
53 = 125 , soHere are the parts of a root
Square roots have index 2, which is not shown
51253
N th root
There are more roots then square or cubes.
abthenbaIf nn ,
3243;2433 55
How do I know if the answer is positive or negative
For example:
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
5525 or
Even roots the answer have to come out positive
Even roots
Odd roots
55255 2
282 33 3
3273
Other Roots
Some we will work with later in this class.
numbersimagineryyougives
n
16
00
The ± symbol
± means positive and negative
So
Since x2 is positive, it does not have to be in an absolute value
24 864 xx
Simplify
43 5 p
Simplify
23
43
5
5
p
p
Simplify
5 1510243 ba
Simplify
32
5 1510
3
243
ba
ba
Simplify
4
Simplify
6 6a
Simplify
a
a6 6
Simplify
5 152243 x
Simplify
3
5 15
23
2243
x
x
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
3 38
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
362.3361975407.3383
HomeworkHomework
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#17 – 55 odd, 63#17 – 55 odd, 63
HomeworkHomework
Page 248Page 248
#16 – 58 even#16 – 58 even