sum of rational number and irrational number is
irrational
The sum of a rational number and an irrational number can be either rational or irrational, depending on the specific numbers involved.
For example, if we add the rational number 1/2 to the irrational number √2, we get:
1/2 + √2
This sum is irrational, because it cannot be expressed as a ratio of two integers. The decimal representation of this sum goes on forever without repeating.
On the other hand, if we add the rational number 1/3 to the irrational number π (pi), we get:
1/3 + π
This sum is irrational as well, because π is irrational. However, its exact value is unknown, so we cannot simplify it further. So, we can say that the sum of a rational and irrational number can be either rational or irrational, depending on the specific numbers involved.
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