Final answer:
The sum of two rational numbers is always a rational number, hence the correct choice is Option B: 2/3 + 9.26, which can be expressed as a fraction.
Step-by-step explanation:
The question asks which of the following is rational:
- 3 * π
- 2/3 + 9.26
- √45 + √36
- 14.3 + 5.78765239...
Rational numbers are numbers that can be expressed as the quotient or fraction ⅟ of two integers, where the denominator is not zero. We can examine each option to determine if it is a rational number:
- 3 * π is not rational because π (pi) is an irrational number.
- 2/3 + 9.26 is rational because it can be expressed as a fraction.
- √45 + √36 is rational because √36 is a perfect square and equals 6, and while √45 is not a perfect square, it can be simplified to 3√5, which is the sum of a rational and an irrational number, thus irrational.
- 14.3 + 5.78765239... appears to be irrational because the digits after the decimal point do not terminate or form a repeating pattern.
Therefore, the answer is Option B: 2/3 + 9.26 because it is the sum of two rational numbers, and the sum of two rational numbers is always a rational number.