What causes errors in experimental calculations of x?

[j-lee00]

x = s(sqrt((2(a+b))/zab)

There is error in s, a and b

show the required result is

$$\Delta$$x/x = sqrt( (1/(4ab)^2)*[(b$$\Delta$$a/a)^2+(a$$\Delta$$b/b)^2]+($$\Delta$$s/s)^2

 

[HallsofIvy]

What happened to the "z" in the denominator? I don't see it in the result? Is it a typo?

Try this: take the logarithm of both sides so
ln(x)= ln(s)+ (1/2)[ln(2)+ ln(a+b)- ln(a)- ln(b)- ln(z)]

Now take the differential:
dx/x= ds/s+ (1/2)[(da+db)/(a+b)- da/a- db/b- dz/z] and replce each "d" with "$\Delta$.

 

[j-lee00]

z has no error associated with it