anonymous one year ago 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

1. jim_thompson5910

the pythagorean theorem is a^2 + b^2 = c^2

2. 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

3. jim_thompson5910

on the right side, the square and square root cancel, leaving just c behind

4. jim_thompson5910

so that's why $\Large c = \sqrt{a^2 + b^2}$

5. 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

6. anonymous

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7. jim_thompson5910

there won't be a plus/minus symbol

8. jim_thompson5910

there shouldn't be one

9. jim_thompson5910

it's simply $\Large c = \sqrt{a^2 + b^2}$

10. 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

11. anonymous

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12. jim_thompson5910

they are the same, but you shouldn't have a +- at all |dw:1433639149567:dw|

13. 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?

14. jim_thompson5910

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15. jim_thompson5910

c represents the length of the hypotenuse (the longest side of a right triangle)

16. 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

17. jim_thompson5910

so instead of saying c = plus or minus 10 we just say c = +10 or just c = 10

18. jim_thompson5910

the c = minus 10 = -10 makes no sense

19. anonymous

oh i see. ok thanks!

20. jim_thompson5910

you're welcome