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The sum of a rational number and an irrational number is always irrational because it results in a non-terminating decimal.

What are rational and irrational numbers?

  • Rational numbers are numbers that can be represented by fractions, such as terminating decimals.
  • Irrational numbers are numbers that cannot be represented by fractions, such as non-terminating decimals and non-exact roots.

The sum of a terminating decimal with a non-terminating decimal always results in a non terminating decimal, that is, the sum of a rational number with an irrational number is always irrational.

More can be learned about rational and irrational numbers at brainly.com/question/17232771

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adioabiola

The sum of a rational number and an irrational number always results in an irrational number because the rational number assumption yields a contradiction.

Why is the sum of a rational number and an irrational number is always irrational?

Upon summing the two type of numbers, rational and irrational number, assuming the result upon rearrangement to be a rational number implies a contradiction.

Hence, the basic premise for the conclusion that the sum of a rational and an irrational number yields an irrational number is because, the other way round implies a contradiction.

Read more on rational and irrational numbers;

https://brainly.com/question/20400557

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