Final answer:
To determine which options result in a rational number, we need to analyze each expression. Options a) and b) result in rational numbers.
Step-by-step explanation:
To determine which of the given options result in a rational number, we need to understand what a rational number is. A rational number is any number that can be expressed as a fraction of two integers (a/b), where b is not zero.
a) A + 5: Rational - This expression involves adding a variable 'A' to a constant '5'. Since both 'A' and '5' are integers, the result will always be rational.
b) 12: Rational - Since 12 is an integer, it can be expressed as a fraction with a denominator of 1, making it a rational number.
c) 140 + √2: Irrational - The expression involves adding a constant '140' to the square root of '2'. The square root of 2 is an irrational number because it cannot be expressed as a fraction of two integers, so the result is irrational.
d) √2: Irrational - The square root of 2 is an irrational number for the same reasons mentioned in option c, so the result is irrational.
Therefore, the options that result in a rational number are a) A + 5 and b) 12.