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Number Theory
Level
1
True or False?
The sum of a rational number and an irrational number must be an irrational number.
False
True
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1 solution
A number is irrational when it can not be written as a fraction with integer components. It, therefore, must have infinite decimal places without repetition. Adding a finite or a repeating decimal does not make a difference, as it is finite or makes the same changes everywhere. Therefore the answer must be T r u e .