What Is the Relative Uncertainty in the Square Root of a Measured Distance?

[unequal]

Homework Statement

A distance R is measured to be 4.000±0.002 m
What is the relative uncertainty in the square root of R?

Homework Equations

Relative uncertainty is the ratio of the absolute uncertainty of a measurement to the best estimate. It expresses the relative size of the uncertainty of a measurement (its precision).

relative uncertainty = absolute uncertainty / best estimate of value x 100%.
So the abosulute is 0.002, where estimated value of R is 4 m

The Attempt at a Solution

all I got is that the square root of R is 2 m, but relative uncertainity of R is 0.002 / 4, however when I square root R, I don't know how I reflect the change in the +-0.002 m.

 

[unequal]

one more piece of info I believe is correct

If say, I had to calculate the relative uncertainty of R^2, then I could write R^2 as R x R, and when multiplying or dividing, I realize I have to add the relative uncertainties, Therefore, the relative uncertainty of R^2 is 0.002 + 0.002 = 0.004 (or 0.4%)

I can not reflect this situation if using R^(1/2), because I do not know what to add...

any suggestions?

thanks

 

[unequal]

when i said "Therefore, the relative uncertainty of R^2 is 0.002 + 0.002 = 0.004 (or 0.4%)" i meant to say, the relative uncertainty of R^2 is 0.002/4 + 0.002/4 = 0.0005 or 0.05%.

 

[unequal]

i am still relatively uncertain about how to do this question

any suggestions would be great!

 

[unequal]

ive looked into this more, and if R was already the squareroot, and I know that squaring it would have to give 0.0005, that would mean R x R = R^2, which addes 2 values to give 0.0005, which would be 0.00025 + 0.00025,

so would the answer to my very original question be 0.00025?? (A distance R is measured to be 4.000±0.002 m
What is the relative uncertainty in the square root of R?)

please could someone help