Verified answer

Not precisely. b would equal +sqrt(c^2-a^2) or - sqrt(c^2-a^2).

Yes

b=√c^2-a^2 (I'm assuming the square root is over both) square both sides, that gives you

b^2=c^2-a^2 now add a^2 to both sides

a^2 + b^2 = c^2