text: Homework Help
  
  # the square root of 243x^13
  
  schooledmom | Salutatorian
  
  Posted June 20, 2013 at 1:56 PM via web
  
  dislike 1 like
  
  the square root of 243x^13
  
  Tagged with algebra 1, math
  
  llltkl | College Teacher | Valedictorian
  
  Posted June 20, 2013 at 2:34 PM (Answer #1)
  
  dislike 1 like
  
  `sqrt (243x^13)=(243x^13)^(1/2)` (by changing the radical form into exponent form)
  
  `=(243)^(1/2)*(x^13)^(1/2)`  (applying `(xy)^m=x^m*y^m` )
  
  `=(243)^(1/2)*x^(13/2)`  (applying `(x^m)^n = x^(mn)` )
  
  `=(3*3*3*3*3)^(1/2) *(x^(13/2))`
  
  = `3^(5/2)*x^(13/2)`
  
  =`9sqrt3*x^6sqrtx ` (expressing in the radical form again)
explanation: The document contains a math question and its corresponding answer. The question is about finding the square root of \( 243x^{13} \), and the answer provides a step-by-step solution to simplify the expression.
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  1. Briefly describe the document and mention if it contains a question or a question and answer.
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distilabel_metadata.role: system
distilabel_metadata.content: Homework Help
  
  # the square root of 243x^13
  
  schooledmom | Salutatorian
  
  Posted June 20, 2013 at 1:56 PM via web
  
  dislike 1 like
  
  the square root of 243x^13
  
  Tagged with algebra 1, math
  
  llltkl | College Teacher | Valedictorian
  
  Posted June 20, 2013 at 2:34 PM (Answer #1)
  
  dislike 1 like
  
  `sqrt (243x^13)=(243x^13)^(1/2)` (by changing the radical form into exponent form)
  
  `=(243)^(1/2)*(x^13)^(1/2)`  (applying `(xy)^m=x^m*y^m` )
  
  `=(243)^(1/2)*x^(13/2)`  (applying `(x^m)^n = x^(mn)` )
  
  `=(3*3*3*3*3)^(1/2) *(x^(13/2))`
  
  = `3^(5/2)*x^(13/2)`
  
  =`9sqrt3*x^6sqrtx ` (expressing in the radical form again)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding answer. The question is about finding the square root of \( 243x^{13} \), and the answer provides a step-by-step solution to simplify the expression.
  
  Label: question-and-answer