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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
Radical
symbol
3
64
radicand
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
Radical Facts:



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!
Radicals with Fractions

Keep your cool! It is
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
ANSWER!
Rational or Irrational, that is the
question?


Some radicals come
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.