# Uncertainty as power.

1. Dec 31, 2012

### arierreF

1. The problem statement, all variables and given/known data

Book: Introduction to error analysis, Taylor

In page 66, quick check 3.8

If you measure x = 100$\pm$ 6, what should you report for $\sqrt{x}$with its uncertainty.

2. Relevant equations

Rule for uncertainty as power:
$\frac{∂q}{|q|}$ = |n|$\frac{∂x}{|x|}$

where $q = x^{n}$

3. Attempt

So our function is q = $x^{\frac{1}{2}}$

then σq = 0,3. (as in solution)

The problem that is killing me is if i decide to use the general rule for error propagation, the result is different.

Using that rule:

|σq| = |$\frac{∂q}{|x|}| Δx = | \frac{1}{2\sqrt{x}} |Δx$
That gives:

|σq| ≈ 0,3

After all, the problem is correct. It was just bad calculations.

I do not to know how to delete topics. :/

Last edited: Dec 31, 2012