A Below is a proof showing that the sum of a rational number and an irrational number a 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
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 a an irrational number is irrational.
Which of the following best completes the proof?
• it is the sum of two rational numbers
• it is the sum of two irrational numbers
• it represents a non-terminating, non-repeating decimal.
C its terms cannot be combined. Mom