text: Survey
  
  * Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
  
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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.
  ```
  Related documents
explanation: The document is a transcript or educational material that explains the concept of square roots and cube roots, including their properties and how to compute them. It also touches on the distinction between rational and irrational numbers. The document does not contain a specific question or a question-and-answer pair but rather provides a series of explanations and examples.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Survey
  
  * Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
  
  Document related concepts
  
  Positional notation wikipedia , lookup
  
  Location arithmetic wikipedia , lookup
  
  Vincent's theorem wikipedia , lookup
  
  Fundamental theorem of algebra wikipedia , lookup
  
  Elementary mathematics wikipedia , lookup
  
  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.
  ```
  Related documents
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a transcript or educational material that explains the concept of square roots and cube roots, including their properties and how to compute them. It also touches on the distinction between rational and irrational numbers. The document does not contain a specific question or a question-and-answer pair but rather provides a series of explanations and examples.
  
  Label: no-question