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Estimating implies that the number is approximate to the desired value so any number squared that is close to the desired estimation would be considered close enough. Rounding off is a form of estimating and has a set of rules that accompany it. For simple estimating, (non-medical, hazardous items not included) like "what is the square root of 169". it would be about 13X13 or 13 squared. Get closer by finding the factors of 169. and simplify.
Estimating one of them is equivalent to estimating the other.
No, it is not. Estimating may be rounding but need not be.
No. Measuring is getting an exact length. Estimating is guessing what the length is
One strategy is estimating the factors the other i don't know