Final answer:
To identify irrational numbers, look for non-repeating, non-terminating decimals and numbers that cannot be expressed as a fraction of two integers. Use graphical methods and logical steps to solve problems, simplify algebra, and check reasonableness, while maintaining practical precision in estimations.
Step-by-step explanation:
To identify the irrational numbers from the given answer choices, you need to recognize that irrational numbers cannot be expressed as a simple fraction or ratio of two integers. Irrational numbers also have non-repeating, non-terminating decimal expansions. Examples of irrational numbers include the square roots of non-perfect squares, pi (π), and the natural logarithm base (e).
When solving problems graphically, it's often useful to visually interpret data and make estimations. For instance, if you know that one half of one half is one quarter, you can often back-out the answer through similar logical steps. Remember to eliminate terms wherever possible to simplify the algebra and always check the answer to see if it is reasonable.
Finally, in gathering or interpreting data, recognize that precision is subject to the context of the problem. In practical scenarios, such as estimating the area of a circle drawn in sand, commit to a level of precision that is practical, but do not overburden with unnecessary decimal places for estimation.