anonymous
  • anonymous
pythagorean theorem: C = √a^2 + √b^2 Should c = √a^2 + √b^2 have a +- symbol in front of the c? Why or why not? @jim_thompson5910
Mathematics
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katieb
  • katieb
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jim_thompson5910
  • jim_thompson5910
the pythagorean theorem is a^2 + b^2 = c^2
jim_thompson5910
  • jim_thompson5910
if you apply square roots to both sides, you get \[\Large a^2 + b^2 = c^2\] \[\Large \sqrt{a^2 + b^2} = \sqrt{c^2}\] notice how there is one root on the left side and it covers ALL of the left side
jim_thompson5910
  • jim_thompson5910
on the right side, the square and square root cancel, leaving just c behind

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jim_thompson5910
  • jim_thompson5910
so that's why \[\Large c = \sqrt{a^2 + b^2}\]
jim_thompson5910
  • jim_thompson5910
and c is some distance c is never negative so you don't have to worry about the plus/minus here. just focus on the plus
anonymous
  • anonymous
|dw:1433638788963:dw|
jim_thompson5910
  • jim_thompson5910
there won't be a plus/minus symbol
jim_thompson5910
  • jim_thompson5910
there shouldn't be one
jim_thompson5910
  • jim_thompson5910
it's simply \[\Large c = \sqrt{a^2 + b^2}\]
jim_thompson5910
  • jim_thompson5910
and it is NOT this \[\Large c = \pm\sqrt{a^2 + b^2}\] the minus implies that we have negative distance which doesn't make sense
anonymous
  • anonymous
|dw:1433638938313:dw|
jim_thompson5910
  • jim_thompson5910
they are the same, but you shouldn't have a +- at all |dw:1433639149567:dw|
anonymous
  • anonymous
yea, its just that the question is asking if the +- should be in front of the c, why or why not. but if its the same with the +- on either side, then whats the reason for not putting the sign?
jim_thompson5910
  • jim_thompson5910
|dw:1433639457958:dw|
jim_thompson5910
  • jim_thompson5910
c represents the length of the hypotenuse (the longest side of a right triangle)
jim_thompson5910
  • jim_thompson5910
any time we talk about lengths or distances, they are either 0 or some positive number they are NEVER ever negative. Negative distance or length doesn't make any sense so that's why c is never negative
jim_thompson5910
  • jim_thompson5910
so instead of saying c = plus or minus 10 we just say c = +10 or just c = 10
jim_thompson5910
  • jim_thompson5910
the c = minus 10 = -10 makes no sense
anonymous
  • anonymous
oh i see. ok thanks!
jim_thompson5910
  • jim_thompson5910
you're welcome

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