#### Transcript Symbols

```Symbols
Defn: a is the positive (or principal) square root of a.
It is the positive number whose square is a.
Every radical expression contains three parts:
index
symbol
3
64
This expression represents the number we must cube to get 64.
Because 43  64 , we say that 3 64  4
NOTE: When an index is not shown, it is assumed to be a 2.
You might want to memorize the first
few square and cube roots?
1 1
4 2
9 3
3
1 1
3
82
3
27  3
3
64  4
3
125  5
16  4
25  5
36  6
49  7
64  8
81  9
100  10
121  11
144  12



The even power of a
real number is always
4
positive or zero. (2)   2 2 2 2  16
Thus, an even root of a
negative number is
4
16 
undefined on the set of
real numbers.
An odd root of a
3
negative number will

8


2
always be negative.
Keep It Straight!
The negative square root
of 9 is -3!
 9  3 Where the square root of
9 
a negative number
is undefined on the set of
real numbers.
Now,You’ve Got It!

easy.
4
4 2


25
25 5
Just take the
square root
of the
numerator AND
take the square
root of the
denominator!
Examples:
 16   4
121  11
4
81  3
3
27  3
0 0
Remember: it is okay to have
a negative radicand if the root
odd.. We just get a NEGATIVE
Rational or Irrational, that is the
question?


out nice and easy..
Others not so nice..
Since there is no
number that raised to
the third power gives
us 12, our calculator
has to approximate it:
 7  7  7  7   7
4
2401 
3
12  2.289428485...
4
If the decimal approximation terminates or repeats it is a rational
number.
If the decimal approximation does not terminate or repeat, it is
called an irrational number.
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