Maybe a dumb question on standard error in equations

[JazzyJones]

Homework Statement

I am using a value of change in y say 12.10 cm + or - .06cm.

I am trying to find velocity using the formula
v= sqrt(2*g*change in y)

how do I evaluate this equation with my standard error? because I can't just add or subtract the .06cm after since I will have a value for velocity now.

Homework Equations

The Attempt at a Solution

 

[Spinnor]

Can you just plug in 12.10 cm to get v and then plug in 12.10 cm + .06cm and 12.10 cm - .06cm to figure out the error in v?

 

[JazzyJones]

i'm not sure if this was correct but, I plugged in the value with + then plugged in te value with -. Average the two values, and did + or - the difference between the two

 

[haruspex]

i'm not sure if this was correct but, I plugged in the value with + then plugged in te value with -. Average the two values, and did + or - the difference between the two

That'll work. The algebraic way is to approximate sqrt(x + dx) = sqrt(x)sqrt(1+dx/x) as sqrt(x)(1+dx/2x) for small dx.