1. Symbols Defn: is the positive (or principal) square root of a.
It is the positive number whose square is a.
Every radical expression contains three parts:
This expression represents the number we must cube to get 64. Because , we say that
index
Radical
symbol
radicand
NOTE: When an index is not shown, it is assumed to be a 2.

2. You might want to memorize the first few square and cube roots?

3. Radical Facts:
The even power of a real number is always positive or zero.
Thus, an even root of a negative number is undefined on the set of real numbers.
An odd root of a negative number will always be negative.

4. Keep It Straight! Now,You’ve Got It!
The negative square root of 9 is -3!
Where the square root of a negative number
is undefined on the set of real numbers.
Now,You’ve Got It!

5. Radicals with Fractions
Keep your cool! It is easy.
Just take the square root
of the numerator AND
take the square root of the
denominator!

6. Examples: Remember: it is okay to have a negative radicand if the root
odd.. We just get a NEGATIVE
ANSWER!

7. 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:
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.