Final answer:
The sum of 25 and 2√7 is 25 + 2√7, an expression which cannot be further simplified and is irrational because the sum of a rational and an irrational number is always irrational. The correct answer is B. 25 + 2√7; Irrational.
Step-by-step explanation:
To find the sum of 25 and 2√7 in simplest form, we simply add the two given numbers together because they are not like terms and cannot be simplified further. The result is 25 + 2√7. This expression consists of a rational number, 25, and an irrational number, 2√7. An irrational number is one that cannot be expressed as a ratio of two integers and its decimal form is non-terminating and non-repeating. The square root of a non-perfect square (like 7) is an irrational number. Therefore, when we add a rational and an irrational number, the sum is also irrational.
Thus, the correct answer is B. 25 + 2√7; Irrational.
To determine the nature of the sum, we don't need a common denominator as that concept applies to adding fractions. We simply observe the properties of rational and irrational numbers. In addition, rounding or evaluating an expression to a certain decimal place is not needed here, nor is the concept of components and resultant as in physics or simplifying algebraic expressions with like terms. It's important to check the answer, however, to ensure it is reasonable and follows the mathematical principles.