When dealing with significant figures in calculations involving square roots, you generally follow the rule that the result should have the same number of significant figures as the number with the fewest significant figures in the calculation.
Here's a step-by-step guide:
Determine the number with the fewest significant figures among the values involved in the square root calculation.
Take the square root of that number using your preferred method or calculator.
Round the result to match the number of significant figures of the original number.
Let's consider an example:
Suppose you want to find the square root of 12.5.
The number 12.5 has three significant figures.
Taking the square root of 12.5 yields approximately 3.54.
Since the original number has three significant figures, round the result to three significant figures, giving you 3.54 as the final answer.
Remember that significant figures are a way to express the precision or uncertainty of a measured or calculated value, and they help maintain consistency in the reporting of results throughout calculations.