Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

there won't be a plus/minus symbol

Answer 7

there shouldn't be one

Answer 8

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

Answer 9

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