Below is a proof showing that the sum of a rational number and an irrational number is an irrational number. Let a be a rational number and b be an irrational number.
Assume that a + b = x and that x is rational.
Then b = x - a = x + (-a).
X + (-a) is rational because
However, it was stated that b is an irrational number. This is a contradiction.
Therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational
number.
In conclusion, the sum of a rational number and an irrational number is irrational.
Which of the following best completes the proof?
O it is the sum of two rational numbers.
O it is the sum of two irrational numbers.
it represents a non-terminating, non-repeating decimal.
its terms cannot be combined.