Verified answer

Square root is equivalent to raising to the power 1/2. For any power (e.g. 2 or 1/2) you multiply the %uncertainty by the power.

E.g. X = (50+/-1) units

%uncertainty in X = 100 x 1/50 = 2%

%uncertainty in X^2= 2 x 2% = 5%

%uncertainty in X^(1/2)= 1/2 x 2% = 1%

For logarithms and antilogs, it depends on the base used. I'm not too hot on these, so see link.

Your teacher and/or text book should cover this if you are expected to handle this sort of calculation.

You can look up 'Error Propagation' to find the theory behind this - you need to understand a bit of calculus and Taylor series.

1)

What happens when the square root thing is involved?

The happennings are Shown when you have,some Questios.

2)

What happens when the log (and -log) thing is involved?

Here, again,

The happennings are Shown when you have,some Questios.

The taylor Expansion is the answer.

so take eg log(a+h)=loga+h/a

log(a-h)=loga-h/a

so if uncertainty in a is h then uncertainty in loga is h/a or -h/a

similarly for sqrt(a) sqrt(a+h)=sqrt(1+h/a)sqrt(1+h/a)^1/2=sqrt.(1+h/2a) so the uncertainty in sqrt is h/2sqrt(a) etc.

Ivan