Final answer:
Simplifying radical expressions is crucial for adding or subtracting like terms and ensuring ease of calculation and accuracy. It involves finding a common form for radicals and using principles like scientific notation and exponent rules.
Step-by-step explanation:
It is important to simplify radical expressions before adding or subtracting because it allows us to combine like terms and to ensure we are working with the simplest form of the numbers, making calculations easier and more accurate. When we simplify radicals, we are often able to find common terms that can be added or subtracted, which is analogous to having to ensure that fractions have a common denominator before they can be combined.
Simplifying the algebra by eliminating terms wherever possible is crucial for both understanding the concept behind the numbers and for computational ease. Also, utilizing scientific notation and understanding the properties of exponents, like how the product of powers can be solved by adding exponents, can greatly simplify calculations. Finally, always check the answer to see if it is reasonable, as this helps to consolidate the mastery over the conceptual understanding necessary for solving such problems.