A is a rational number and x is an irrational number. How that a+x is irrational number? A is rational number and x is irrational number. How to prove that a+x is irrational number?

A is a rational number and x is an irrational number. How that a+x is irrational number? A is rational number and x is irrational number. How to prove that a+x is irrational number?

Because rational numbers can be represented on the number axis, irrational numbers can not, when rational numbers and rational numbers add, the answer can still be represented on the number axis, but rational numbers add irrational numbers can not be represented on the number axis, so a+x = irrational number

How to prove that irrational number plus rational number equals irrational number

Inverse method.
Let p be irrational, q be rational
Let r=p+q
If r is a rational number, then p = r - q
Note whether two rational numbers are subtracted or rational, so the right side of the equation above is rational.
On the left are irrational numbers.
Surface contradiction
So r can only be an irrational number.
Certificate completed.

In any case.
Let p be irrational, q be rational
Let r=p+q
If r is a rational number, then p = r - q
Note whether two rational numbers are subtracted or rational, so the right side of the equation above is rational.
On the left are irrational numbers.
Contradiction.
So r can only be an irrational number.
Certificate completed.