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  Transcript
  ```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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